Quote Originally Posted by Duke of Gloucester
Light does have mass. The mass of a given photon is hf/c^2 where h is Plancks constant, c is the speed of light and f is the frequency of the photon. E=mc^2 tells us that mass and energy are basically the same thing, and since photons have energy, they must have mass.
Photons do not have a mass, all the mass is in the form of energy. They do however have momentum.

If they had any mass then they would have infinite mass at the speed of light.

As for the light being bent by gravity, it is the very fabric of space being warped that causes that. The effect would be stronger if photons had a tiny mass... and the amount that the light bends due to gravity would change dependent on the mass... since they all have zero rest mass, the light is all bent by the same amount.

If photons had different masses then gravitational lensing would cause chromatic dispersion.