How come photons and...

[hackenslash]

Photons have no rest mass, but they are never at rest, so they do have mass, in the form of kinetic energy via E=mc2.

As for the original question, photons don't curve, they follow a geodesic, which is a straight line through curved space. Think of it like travelling on Earth. If youo wanted to travel from New York to London via the shortest route possible, you would have to travel in a straight line. However, the surface of the Earth is curved, so to travel in a straight line would actually involve digging a tunnel through the Earth to get there. When you travel over the surface, you aren't travelling in a straight line, you are following a geodesic (often described as a world-line). This is what photons are doing when they, for example, curve around a star. They are travelling a geodesic, but the space is curved.

It should be noted here what mass actually is, because it's a confusing concept to many, although pretty simple if dealt with properly. What mass is, rigorously treated, is simply resistance to acceleration. When you think of it like that, it's fairly easy to get your head around.