Ah, now I have confused myself by saying "the same happen to mass and energy" so then light does not have to have mass. >_<
Edit: What the hell kind of nonsense did I just write in the previous post!? Obviously I wasn't trying to say that light orbits around the sun, but it came out that way. I guess my point was that sure light travels in a straight line around the space-time 'funnel', but so does mass.
Edit 2: Wait, actually light CAN orbit an object (like a black hole).
http://en.wikipedia.org/wiki/Photon_sphere Well, at least I wasn't completely crazy.
But to answer my own question, no light does not have a mass.