[filospinato]

Theorized to have no rest mass.

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

[kosciusko51]

From the same link, they have experimentally shown that if it has any rest mass, it is very, very small. Right now, there is only a upper bound on the rest mass, which includes no rest mass. When someone puts an lower limit on the mass, then you can say it has mass.