Light travels at the speed of light, and it has mass. Why else would be affected by gravity?
Light indeed does have mass, you can calculate the mass of a photon by using E=MC2 in the form M=E/C2. The energy is related to the frequency (i.e. color)
What light, in general electromagnetic radiation, does not have, is rest mass. The formulae for mass is:
Mass = Rest_mass / sqrt(1 - V2/c2)
where: V2 is the speed squared
C2 is the speed of light (in a vacumn) squared.
From this one can see that as the speed approaches that of light, the denoninator approaches zero and the mass increases without bound (that is infinity) UNLESS the Rest mass itself is zero.