Photons can have momentum, which, when doing relativity, blends together with energy into the momentum 4-vector [http://en.wikipedia.org/wiki/Four-momentum]. Relativity also asserts that energy and mass are related [http://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relatio...], so you can imagine how we could talk about the "mass" of anything with energy or momentum.

Fun fact: One of the ways physicists are looking for Higgs is by looking for bumps in the "invariant mass" spectrum of LHC events with 2 photons!

Thanks - I'll read up. I've long interpreted E=mc^2 to mean not just that energy and mass are interchangeable, that energy and mass are one and the same. What I can't quite get my head around yet (just need to read up more) is how they figured out something about the rest mass of a photon - something about using superconducting rings or something like that. (Because photons aren't generally at rest, and they don't accelerate, right?)