Why are pulsar's radiation beams collimated? Every picture of a pulsar I see shows a very collimated radiation beam. What is the mechanism generating such a collimation?
Note: I am not talking about "relativistic jets". I am talking about radiation, not matter.
 A: When charged particles are accelerated away from the magnetic poles of the neutron star, they are tied to helical paths along the magnetic field lines by the Lorentz force (see for example here). Since the particles are travelling in helical paths they are still accelerating and therefore emit electromagnetic radiation - known as synchrotron radiation. This radiation is emitted by particles that are highly relativistic from our point of view, in which case the rest frame electric and magnetic fields of the emitted radiation are (Lorentz) transformed according to special relativity, resulting in the phenomena of Doppler boosting and Doppler beaming in the direction in which the particles are travelling.
The basic mechanism is described here, some formulae are given here, but the basic result is that radiation emitted by an accelerating charged particle is concentrated into a narrow cone in the direction of travel, with beaming opening angle that is approximately $2/\gamma$ (in radians), where $\gamma= (1-v^2/c^2)^{-1/2}$, is the relativistic Lorentz factor. In practice for the example of a pulsar, I think this angle is so small that this isn't what determines the overall collimation of the radiation. The actual degree of collimation would depend on how far the magnetic field lines have diverged between leaving the neutron star surface and where the bulk of the radiation is emitted. These issues and the exact beaming mechanisms are not solved problems.
The exact same phenomenon is found in synchrotron accelerators - which is where the name comes from. Here, charged particles emit radiation as they are bent around in their paths by strong magnets. This is a nuisance energy loss if you are trying to accelerate the particles, or a useful feature if you wish to use the synchrotron radiation to do experiments.
Getting back to your original question, you attempt to separate out the issue of a relativistic jet of matter from a collimated beam; but they go hand-in-hand. Radiation emitted from matter moving at relativistic speeds will always be boosted and beamed (i.e. collimated) in the forward direction.
A: Magnetic fields.
The beams are generated from charge particles moving in magnetic fields. The pulsar is the result of a large star collapsing and the magnetic field of the original star is compressed, making a very strong field. 

A: From FURTHER EVIDENCE FOR COLLIMATED PARTICLE BEAMS FROM PULSARS AND PRECESSION (2007):
"An overwhelming majority of the observers and theorists interpreting
these observations seem to suggest and endorse the following
basic picture. The jetlike features nearly along the symmetry
axis, bisecting the arcs and the diffuse glow spread about them, are
identified with collimated outflows of relativistic particles along the
spin axis of the central compact remnant, a pulsar."
Similar to the magnetic axis of the earth, but in this case, of the pulsar.
