Are W & Z bosons virtual or not? W and Z bosons are observed/discovered. But as force carrying bosons they should be virtual particles, unobservable? And also they require to have mass, but if they are virtual they may be off-shell, so are they virtual or not. 
 A: All observed particles are real particles in the sense that, unlike virtual particles, their properties are verifiable by experiment. In particular, W and Z bosons are real but unstable particles at energies above the energy equivalent of their rest mass. They also arise as unobservable virtual particles in scattering processing exchanging a W or Z boson, though the existence of a corresponding exchange diagram is visible experimentally as a resonance.
Virtual particles and unstable (i.e., short living) particles are conceptually very different entities.
Since there seems to be a widespread confusion about the meaning of the terms (and since Wikipedia is quite unreliable in this respect) let me give precise definitions of some terms:
A stable, observable (and hence real in the sense specified above) particle has a real mass $m$ and a real 4-momentum $p$ satisfying $p^2=m^2$; one also says that it is on-shell. For such particles one can compute S-matrix elements, and according to quantum field theory, only for such particles. In perturbative calculations, stable particles correspond precisely to the external lines of the Feynman diagrams on which perturbation theory is based. Only a few elementary particles are stable, and hence can be associated with such external lines. (However, in subtheories of the standard model that ignore some interactions, particles unstable in Nature can be stable; thus the notion is a bit context dependent.)
A virtual particle has real momentum with $p^2\ne m^2$ (one also says that they are off-shell), and cannot exist as it would violate energy conservation. In perturbative calculations, virtual particles correspond precisely to the internal lines of the Feynman diagrams on which perturbation theory is based, and are only visual mnemonic for integrations over 4-momenta not restricted to the mass shell. In nonperturbative methods for calculating properties of particles, there is no notion of virtual particles; they are an artifact of perturbation theory. 
Virtual particles are never observable. They have no properties to which one could assign in any formally meaningful way a dynamics, and hence some sort of existence in time. In particular, it is meaningless to think of them as short-living objects. (Saying they pop in and out of existence for a time allowed by the uncertainty pronciple has no basis in any dynamical sense - it is pure speculation based on illustrations for the uneducated public, and from a widespread misunderstanding that internal lines in Feynman diagrams describe particle trajectories in space-time). 
All elementary particles may appear as internal lines in perturbative calculations, and hence possess a virtual version. For a more thorough discussion of virtual particles, see 
Chapter A8: Virtual particles and vacuum fluctuations of my 
theoretical physics FAQ.
An unstable observable (and hence real in the sense specified above) particle has a complex mass $m$ and a complex 4-momentum $p$ satisfying $p^2=m^2$. (One shouldn't use the term on-shell or off-shell in this case as it becomes ambiguous). The imaginary part of the mass is relatied to the halflife of the particle. At energies below the energy $E= Re\ mc^2$, unstable elementary particles are observable as resonances in cross sections of scattering processes involving their exchange as virtual particle, while at higher energies, they are observable as particle tracks (if charged) or as gaps in particle tracks; in the latter case identifiable by the tracks of their charged products.
For unstable particles one can compute S-matrix elements only in approximate theories where the particle is treated as stable, or by analytic continuation of the standard formulas for stable particles to complex energies and momenta.
A: [Edit June 2, 2016:
A significantly updated version of the material below can be found in
the two articles 
https://www.physicsforums.com/insights/misconceptions-virtual-particles/
and
https://www.physicsforums.com/insights/physics-virtual-particles/
]
Let me give a second, more technical answer.
Observable particles.
In QFT, observable (hence real) particles of mass $m$ are conventionally
defined as being associated with poles of the S-matrix at energy 
$E=mc^2$ in the rest frame of the system 
(Peskin/Schroeder, An introduction to QFT, p.236). If the pole is at a 
real energy, the mass is real and the particle is stable; if the pole 
is at a complex energy (in the analytic continuation of the S-matrix 
to the second sheet), the mass is complex and the particle is unstable. 
At energies larger than the real part of the mass, the imaginary part 
determines its decay rate and hence its lifetime 
(Peskin/Schroeder, p.237); at smaller energies, the unstable particle 
cannot form for lack of energy, but the existence of the pole is 
revealed by a Breit-Wigner resonance in certain cross sections.
From its position and width, one can estimate the mass and the lifetime 
of such a particle before it has ever been observed. 
Indeed, many particles listed in the tables 
http://pdg.lbl.gov/2011/reviews/contents_sports.html by the Particle 
Data Group (PDG) are only resonances.

Stable and unstable particles.
A stable particle can be created and annihilated, as there are 
associated creation and annihilation operators that add or remove 
particles to the state. According to the QFT formalism, these 
particles must be on-shell. This means that their momentum $p$ is 
related to the real rest mass $m$ by the relation $p^2=m^2$.
More precisely, it means that the 4-dimensional Fourier transform of the time-dependent single-particle wave function associated with it has a support that satisfies the on-shell relation $p^2=m^2$. There is no need for this wave function to be a plane wave, though these are taken as the basis functions between the scattering matrix elements are taken.
An unstable particle is represented quantitatively by a so-called 
Gamov state (see, e.g., http://arxiv.org/pdf/quant-ph/0201091.pdf), 
also called a Siegert state 
(see, e.g., http://www.cchem.berkeley.edu/millergrp/pdf/235.pdf) 
in a complex deformation of the Hilbert space of a QFT, obtained by 
analytic continuation of the formulas for stable particles.
In this case, as $m$ is complex, the mass shell consists of all complex 
momentum vectors $p$ with $p^2=m^2$ and $v=p/m$ real, and states are 
composed exclusively of such momentum vectors. This is the 
representation in which one can take the limit of zero decay, in which 
the particle becomes stable (such as the neutron in the limit of 
negligible electromagnetic interaction), and hence the representation 
appropriate in the regime where the unstable particle can be observed 
(i.e., resolved in time).
A second representation in terms of normalizable states of real mass 
is given by a superposition of scattering states of their decay 
products, involving all energies in the range of the Breit-Wigner 
resonance. In this standard Hilbert space representation, the unstable 
particle is never formed; so this is the representation appropriate in 
the regime where the unstable particle reveals itself only as a 
resonance.
The 2010 PDG description of the Z boson, 
http://pdg.lbl.gov/2011/reviews/rpp2011-rev-z-boson.pdf
discusses both descriptions in quantitative detail (p.2: Breit-Wigner 
approach; p.4: S-matrix approach).
(added March 18, 2012): 
All observable particles are on-shell, though the mass shell is real 
only for stable particles.

Virtual (or off-shell) particles.
On the other hand, virtual particles are defined as internal lines in 
a Feynman diagram (Peskin/Schroeder, p.5, or 
Zeidler, QFT I Basics in mathematics and physiics, p.844).
and this is their only mode of being. In diagram-free approaches 
to QFT such as lattice gauge theory, it is even impossible to make 
sense of the notion of a virtual particle. Even in orthodox QFT one 
can dispense completely with the notion of a virtual particle, as 
Vol. 1 of the QFT book of Weinberg demonstrates. He represents the 
full empirical content of QFT, carefully avoiding mentioning the 
notion of virtual particles.
As virtual particles have real mass but off-shell momenta, and 
multiparticle states are always composed of on-shell particles only, 
it is impossible to represent a virtual particle by means of states. 
States involving virtual particles cannot be created for lack of 
corresponding creation operators in the theory.
A description of decay requires an associated S-matrix, but the in- 
and out- states of the S-matrix formalism are composed of on-shell 
states only, not involving any virtual particle. (Indeed, this is the 
reason for the name ''virtual''.)
For lack of a state, virtual particles cannot have any of the usual 
physical characteristics such as dynamics, detection probabilities, 
or decay channels. How then can one talk about their probability of 
decay, their life-time, their creation, or their decay? One cannot, 
except figuratively!

Virtual states.
(added on March 19, 2012):
In nonrelativistic scattering theory, one also meets the concept 
of virtual states, denoting states of real particles on the second 
sheet of the analytic continuation, having a well-defined but purely 
inmaginary energy, defined as a pole of the S-matrix. See, e.g., Thirring, 
A course in Mathematical Physics, Vol 3, (3.6.11). 
The term virtual state is used with a different meaning in virtual 
state spectroscopy (see, e.g., 
http://people.bu.edu/teich/pdfs/PRL-80-3483-1998.pdf), and denotes 
there an unstable energy level above the dissociation threshold. 
This is equivalent with the concept of a resonance. 
Virtual states have nothing to do with virtual particles, which have 
real energies but no associated states, though sometimes the name 
''virtual state'' is associated to them. See, e.g., 
https://researchspace.auckland.ac.nz/bitstream/handle/2292/433/02whole.pdf; 
the author of this thesis explains on p.20 why this is a misleading 
terminology, but still occasionally uses this terminology in his work.

Why are virtual particles often confused with unstable particles?
As we have seen, unstable particles and resonances are observable and 
can be characterized quantitatively in terms of states.
On the other hand, virtual particles lack a state and hence have no 
meaningful physical properties.
This raises the question why virtual particles are often confused with 
unstable particles, or even identified. 
The reason, I believe, is that in many cases, the dominant contribution 
to a scattering cross section exhibiting a resonance comes from the 
exchange of a corresponding virtual particle in a Feynman diagram 
suggestive of a collection of world lines describing particle creation 
and annihilation. (Examples can be seen on the Wikipedia page for W and 
Z bosons, http://en.wikipedia.org/wiki/Z-boson.)
This space-time interpretation of Feynman diagrams is very tempting 
graphically, and contributes to the popularity of Feynman diagrams 
both among researchers and especially laypeople, though some authors 
- notably Weinberg in his QFT book - deliberately resist this 
temptation.
However, this interpretation has no physical basis. Indeed, a single 
Feynman diagram usually gives an infinite (and hence physically 
meaningless) contribution to the scattering cross section. The finite, 
renormalized values of the cross section are obtained only by summing 
infinitely many such diagrams. This shows that a Feynman diagram 
represents just some term in a perturbation calculation, and not a 
process happening in space-time. Therefore one cannot assign physical 
meaning to a single diagram but at best to a collection of infinitely 
many diagrams. 

The true meaning of virtual particles.
For anyone still tempted to associate a physical meaning to virtual 
particles as a specific quantum phenomenon, let me note that 
Feynman-type diagrams arise in any perturbative treatment of 
statistical multiparticle properties, even classically, as any textbook 
of statistical mechanics witnesses. 
More specifically, the paper 
http://homepages.physik.uni-muenchen.de/~helling/classical_fields.pdf
shows that the perturbation theory for any classical field theory 
leads to an expansion into Feynman diagrams very similar to those for quantum field theories, except that only tree diagrams occur. If the picture of virtual particles derived from Feynman diagrams had any intrinsic validity, one should conclude that associated to every classical field there are classical virtual particles behaving just like their quantum analogues, except that (due to the lack of loop diagrams) there are no virtual creation/annihilation patterns.
But in the literature, one can find not the slightest trace of a suggestion that classical field theory is sensibly interpreted in terms of virtual particles. 
The reaon for this similarity in the classical and the quantum case is that  Feynman diagrams are nothing else than a graphical notation 
for writing down products of tensors with many indices summed via the 
Einstein summation convention. The indices of the results are the 
external lines aka ''real particles'', while the indices summed over 
are the internal lines aka ''virtual particles''. As such sums of 
products occur in any multiparticle expansion of expectations, 
they arise irrespective of the classical or quantum nature of the 
system.

(added September 29, 2012)
Interpreting Feynman diagrams.
Informally, especially in the popular literature, virtual paricles are 
viewed as transmitting the fundamental forces in quantum field theory.
The weak force is transmitted by virtual Zs and Ws. The strong force 
is transmitted by virtual gluons. The electromagnetic force is 
transmitted by virtual photons. This ''proves'' the existence of 
virtual particles in the eyes of their aficionados.
The physics underlying this figurative speech are Feynman diagrams,
primarily the simplest tree diagrams that encode the low order 
perturbative contributions of interactions to the classical limit of 
scattering experiments. (Thus they are really a manifestation of 
classical perturbative field theory, not of quantum fields.
Quantum corrections involve at least one loop.)
Feynman diagrams describe how the terms in a series expansion of the 
S-matrix elements arise in a perturbative treatment of the interactions 
as linear combinations of multiple integrals. Each such multiple 
integral is a product of vertex contributions and propagators, and each 
propagator depends on a 4-momentum vector that is integrated over.
In additon, there is a dependence on the momenta of the ingoing 
(prepared) and outgoing (in principle detectable) particles.
The structure of each such integral can be represented by a Feynman 
diagram. This is done by associating with each vertex a node of the 
diagram and with each momentum a line; for ingoing momenta an external 
line ending in a node, for outgoing momenta an external line starting 
in a node, and for propagator momenta an internal line between two 
nodes. 
The resulting diagrams can be given a very vivid but superficial 
interpretation as the worldlines of particles that undergo a 
metamorphosis (creation, deflection, or decay) at the vertices.
In this interpretation, the in- and outgoing lines are the worldlines 
of the prepared and detected particles, respectively, and the others 
are dubbed virtual particles, not being real but required by this
interpretation. This interpretation is related to - and indeed 
historically originated with - Feynman's 1945 intuition that all 
particles take all possible paths with a probability amplitute given 
by the path integral density. Unfortunately, such a view is naturally 
related only to the formal, unrenormalized path integral. But there all 
contributions of diagrams containing loops are infinite, defying a 
probability interpretation.
According to the definition in terms of Feynman diagrams, a virtual 
particle has specific values of 4-momentum, spin, and charges, 
characterizing the form and variables in its defining propagator.
As the 4-momentum is integrated over all of $R^4$, there is no mass 
shell constraint, hence virtual particles are off-shell.
Beyond this, formal quantum field theory is unable to assign any 
property or probability to a virtual particle. This would require to 
assign to them states, for which there is no place in the QFT formalism.
However, the interpretation requires them to exist in space and time, 
hence they are attributed by inmagination with all sorts of miraculous 
properties that complete the picture to something plausible. (See, for 
example, the 
Wikipedia article on virtual particles.)
Being dressed with a fuzzy notion of quantum fluctuations, where the 
Heisenberg uncertainty relation allegedly allows one to borrow for a 
very short time energy from the quantum bank, these properties have a 
superficial appearance of being scientific.
But they are completely unphysical as there is neither a way to test 
them experimentally nor one to derive them from formal properties of 
virtual particles. 
The long list of manifestations of virtual particles mentioned in the 
Wikipedia article cited are in fact manifestations of computed 
scattering matrix elements.
They manifest the correctness of the formulas for the multiple 
integrals associated with Feynman diagrams, but not the validity of 
the claims about virtual particles.
Though QFT computations generally use the momentum representation, 
there is also a (physically useless) Fourier-transformed complementary 
picture of Feynman diagrams using space-time positions in place of 
4-momentaa. In this version, the integration is over all of space-time, 
so virtual particles now have space-time positions but no dynamics, 
hence no world lines. (In physics, dynamics is always tied to states 
and an equation of motion. No such thing exists for virtual particles.) 

Can one distinguish real and virtual photons?
There is a widespread view that external legs of Feynman diagrams are 
in reality just internal legs of larger diagrams. This would blur the 
distinction between real and virtual particles, as in reality, every 
leg is internal. 
The basic argument behind this view is the fact that the photons that 
hit an eye (and this give evidence of something real) were produced by 
excitation form some distant object. This view is consistent with 
regarding the creation or destruction of photons as what happens at a 
vertex containing a photon line. In this view, it follows that the 
universe is a gigantic Feynman diagram with many loops of which we and 
our experiments are just a tiny part.
But single Feynman diagrams don't have a technical meaning. Only the 
sum of all Feynman diagrams has predictive value, and the small ones 
contribute most - otherwise we couldn't do any perturbative 
calculations. 
Moreover, this view contradicts the way QFT computations are actually 
used. Scattering matrix elements are always considered between on-shell 
particles. Without exception, comparisons of QFT results with 
scattering experiments are based on these on-shell results. 
It must necessarily be so, as off-shell matrix elements don't make 
formal sense:
Matrix elements are taken between states, and all physical states are 
on-shell by the basic structure of QFT. Thus thestructure of QFT itself 
enforces a fundamental distinction between real particles representable 
by states and virtual particles representable by propagators only.
The basic problem invalidating the above argument is the assumption 
that creation and desctruction of particles in space and time can be 
identified with vertices in Feynman diagrams. They cannot. For Feynman 
diagrams lack any dynamical properties, and their interpretation in 
space and time is sterile. 
Thus the view that in reality there are no external lines is based on
a superficial, tempting but invalid identification of theoretical 
concepts with very different properties.
The conclusion is that, indeed, real particles (represented by external legs) 
and virtual particles (represented by internal legs) are completely separate conceptual entities, clearly distinguished by their meaning. In particular, never turns one into the other or affects one the other.
A: Seems to me there is a confusion between various concepts, let me try to clear it up:


*

*Virtual particle is one that doesn't live forever, at some stage it gets converted to something else. As Jeff points out, none of us lives long enough to tell the difference, so the distinction between virtual and non-virtual is a matter of degree. Particles that live for a long time are declared "real", and particles that decay quickly are called "virtual". These are just names, there is no implication that "virtual" particles don't really exist, like white unicorns and other mythical creatures, those are all real measurable effects you can see with your own eyes...

*Any particle can be either real or virtual, whether or not it is massive, whether or not it is bosonic force carrier, or fermionic matter. There is a sense in which massive particles tend to live shorter life (because they have more opportunities to decay), but this is just a rule of thumb.

*Off-shell can be taken here to be synonymous with "virtual".
Hope that helps.
