Usually this question is meaningless since protons are too small to scatter light, they don't 'look' like anything. However at speeds close to the speed of light it seems they are a 'black disk', kinda like an elongated hockey puck. 

Physicists at the LHC have been smashing high energy protons together for a while now and the data they have gathered has lead to this conclusion by calculating and measuring the cross-section of proton-proton inelastic scattering collisions to that of the total cross-section (elastic plus inelastic). In the collision world of physics, at least at VERY high energies (the asymptotic limit to infinity), elastic and inelastic collisions hold more or less the same meaning, for an inelastic collision the protons absorb eachother and for an elastic collision they scatter off eachother. 

Theoretically at very high speeds relativity tells us that the proton will be 'squished' from length contraction and you can imagine a spherical object being squished down to a flat disk, this is essentially what is being suggested here.

The paper was just accepted to Physical Review Letters about a month ago: http://prl.aps.org/abstract/PRL/v107/i21/e212002

Physorg has a nice article about this as well:

http://www.physorg.com/news/2011-12-physicists-ultrahigh-energy-proton-black-disk.html