Icon wrote:But if they're fundamental particles, then wouldn't they still have mass?
No. Not all fundamental particles have non-zero(rest) mass. Some, like electrons and quarks, have non-zero rest mass, but others, like photons, don't.
There is a difference between rest mass (mass when something is stationary) and relativistic mass (which is rest mass + kinetic energy contributed by Einstein's equation, m=E/c<sup>2</sup>).
Photons have zero rest mass, but they are never stationary, since they always travel at light speed, so their relativistic mass is never zero.