Space orientation of light waves Recently I've started to be really intrigued with the electromagnetic spectrum and bumped into this problem:
According to the wave theory of light (or any electromagnetic wave, really), the magnetic field is perpendicular to the direction of the wave, and the electric field is perpendicular to both the direction of the wave and the magnetic field. So the electric field is vertical (at least according to the pictures I found up) and the magnetic field is horizontal. So far so good.
But is the electric field always vertical? And vertical with respect to what? Gravity?  Are light waves, when viewed from the direction of the wave looking like this '+'? What happens if I rotate the source of light? Will the waves be compiled like this 'x' ? Or is the space orientation of the magnetic and electric waves purely arbitrary? Do they undergo spinning across the vector of the direction of the wave?
Hope I made my point clear. Thanks!
 A: The direction of the electric field is called polarization. The direction of the electrical field in the free space lies in the plan perpendicular to the direction of propagation, and if this direction is unique for all the beam, it is said to be linear polarization. So, for linear polarization, the electric field can point in whatever direction that lies in the plan perpendicular to the direction of propagation. (As a side remark, in some cases there exist also longitudinal e.m. waves, e.g. such waves can be obtained in a resonant cavity.)
But there exist also elliptical polarization, in particular, circular polarization. In this case the polarization is not fixed, it rotates during the time, look in Wikipedia, http://en.wikipedia.org/wiki/Circular_polarization. You will see an animation. There is right polarization, in which case the electrical vector rotates counter-clockwise, and left polarization, in which it rotates clockwise.
A: Vertical with respect to whatever arbitrary set of coordinates you devise.   If most of the pictures you see have the E-field pointing "up", that's just some kind of cultural bias.  The E-field can point in any direction at all.
A: There is a problem with diagrams like this

Yes if that was a physical object and you looked at it end-on it would look like a plus-symbol. However it isn't intended to be interpreted physically like that.
These diagrams shouldn't be interpreted as showing a vertical or horizontal displacement
What is being shown is field strength and direction at a single point over time.
Here's a diagram of circularly polarised light

What you'd see looking into this end-on would be a point (or dot).
A: As has already been said: the orientation of the field drawn in your book is arbitrary. Once you have decided that the wave is say going into the page, then all that is required is that the E-field be drawn on the page (i.e. at right angles to the direction of wave propagation). You can put it up, down, left, right, diagonally, it doesn't matter, it would be a valid representation of an electromagnetic wave. The direction of the B-field would then not be arbitrary. It would have to be drawn in the page (so also at right angles to the wave propagation), at right angles to the E-field, and it must also be the case that the vector product $\vec{E} \times \vec{B}$ points in the direction of wave propagation.
The degrees of freedom for the E-field direction then allow other forms of polarisation. The situation I described is linear polarisation, but so long as the E-field vector stays on the page, it can vary with time, it can rotate, it can get bigger or smaller in amplitude etc.
What controls this behaviour is the way that the wave is produced and how it interacts (interferes) with other electromagnetic waves or with interfaces between different materials. For instance if you produce EM waves from a simple linear, oscillating electric dipole, this will produce linearly polarised light where the E-field oscillates up and down along a single line drawn on the page. On the other hand if I then mix this radiation with light with a perpendicular polarisation that oscillates in phase, I will produce light polarised at some angle in between the two (45 degrees if they are of equal amplitude). On the other hand if one of the two waves I mix lags the other in phase by $\pi/2$ I would produce a rotating electric field vector - circularly polarised light. If it leads by $\pi/2$ the electric field vector rotates the other way.
You can also get unpolarised light where the light is an incoherent mixture of different random polariation states. You could turn (some of) this into polarised light by passing it through a polarising filter or by reflecting the polarised light off a block of glass at the Brewster angle. There are lots of interesting ways to mess about with the polarisation of light!
