By definition, a photon (packet of light) has no mass. However, some people trying to explain some of its more peculiar properties (like the fact that we know it pushes on thing) have established an "upper limit" of a photon's mass at 4 x 10-48 grams (4E-48 g). In any case, they do have momentum, and everyone agrees on that (even though yes, momentum = mass * velocity).
However, the real thing is that light isn't affect by gravity. It's sort of an optical illusion on a stellar scale. The gravity isn't working on the photon, but instead, intense gravitational fields are distorting space-time -- we've all seen the heavy weight being dropped onto a flexible grid and how it "bends space." Well, all of the stars and black holes distort space like that, but three-dimensionally, which is sort of funny to think about.
Anyway, when you light doing strange things, like gravitational lensing, or being "sucked" into a black hole, what's happening is that the photon are just following the new "curvature" of space. If the distortion of space leads them into a black hole, that's where they go. If the distortion kind of refracts light around so that distant objects become visible (gravitational lensing), it's doing it because it's following the "fabric" of space.