Why do photons travel? Photons travel at the speed of light.
Is there a known explanation of this phenomenon, and if yes, what is it? 
Edit:
To be clearer, my question is why do photons travel at all.  Why do they have a speed? 
 A: Kind of as an expansion on what drake said, this can be explained in several ways. For example:
In electromagnetism, we know that Maxwell's equations govern electromagnetic radiation. From Maxwell's equations you can derive the EM wave equation
$$\frac{\partial^2\vec{E}}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2\vec{E}}{\partial t^2}$$
(and the same for $\vec{E}\to\vec{B}$) which has solutions corresponding to waves that travel at light speed. As the quanta of these waves, photons will also travel at light speed.
In special relativity, the energy of a particle is related to its mass via $E = \gamma mc^2$. Photons are massless, but they have finite energy. The only way both of these facts can be true without rendering $E = \gamma mc^2$ outright incorrect is if $\gamma$ is undefined, and since $\gamma = 1/\sqrt{1 - v^2/c^2}$, the only way to make $\gamma$ undefined is to have $v = c$.
A: As other answers have mentioned light in classical electricity and magnetism is described very well by the solutions of Maxwell's equations which combine electrostatics and magnetism and describe a traveling wave of energy propagating at a speed c.
This speed is not arbitrary but, as it comes out from the equations, depends on the electric and magnetic constants of materials or the vacuum:

the magnetic permeability mu_0, and the electric permittivity epsilon_0 , which are well defined numbers in the set of units used and we get the speed of light in vacuum as 299,792,458 meters/second
Photons on the other hand are elementary particles and are necessary at the basic framework where quantum mechanics is the description of nature.
Photons appear in elementary and nuclear interactions, taking away energy and momentum and are seen in subsequent interactions  giving up their energy and momentum. 

In this photo in a bubble chamber gammas are entering from the top and here one has interacted with an atomic electron scattering it away and generated an e+e- pair and a secondary photon, the whole first vertex conserves energy and momentum. We know the existence of the secondary photon because a second e+e- pair was by an interaction with an electron or a nucleus where the transfer of energy to the target was too small to appear in the photo.
So this is experimental evidence that photons travel.  
As a particle at that level it is also a wave, and there exist consistent derivations  of the  formation of the classical  wave  from a large  ensemble of photons.
For mathematical consistency, photons also travel in vacuum  at speed c. 
A: Because photons are light quanta. So the claim 'photons travel at the speed of light' is the same as (or the quantum counterpart of) 'light travel at the speed of light'. It is almost by definition, that is, by definition and by the fact that photons are light quanta.

I am sorry I was not clear. I meant why do they travel at all. – BoD
  24 mins ago

David has answered this question.
A: The electromagnetic wave travels at speed of light which is explained by Maxwell's equations. However, in many cases, electromagnetic wave can also exhibit the particle-like behaviour (wave-particle duality), e.g. Einstein's photoelectric effect, so physicists have to model it as particle, known as photons. So what we know as electromagnetic wave is also particle with common property, i.e. speed. Both theories are correct and we don't know exactly what "it" really is.
In summary, photon is just a model for explaining when electromagnetic wave behaves like particle. Asking why photon travels with speed of light is the same as asking why electromagnetic wave travels with speed of light.
A: Light travels as a wave and interacts as a particle so there seems to be no way to answer the question.
For example, consider a gong. When you strike the gong, sound propagates though air. Photons are the end result of gamma radiation. When you 'bang a gong' that energy is released. 'It' must radiate out. Same as with light energy or photons.
A: Photons, i.e., light, travel at the speed of light because observations have been made that they do so. It is not because of theory. In Physics, observation trumps theory, always. Our theories are always approximations, and must be discarded the moment a correct observation shows them to be untrue. 
