No, they do not.
Theorized to have no rest mass.
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
Ok now.
Photons have a REST mass of zero.
However, photons have an effective mass - since they are never at rest - of hv/(c^2), h=planck’s constant, v=frequency, c=speed of light in vacuume.
As far for neutrinos, experiments indicate that neutrinos have a REST mass of a few eV (electron-volts). That neutrinos change from 1 form of neutrino to another is a consequence of the non-zero REST mass.