Well technically neutrons aren't fundamental particles anyway since they're made up of anti-quarks. That said, a particle doesn't have to have an electric charge to have anti-particle, a particle/anti-particle pair have opposite quantum numbers. A neutrino is neutral yet still has an anti-particle, in this case the quantum numbers are the lepton number and parity. Neutrinos have a +1 lepton number (and are all "left handed"), anti-neutrinos -1 lepton number (and are "right handed").

A photon however is its own anti-particle!

Another interesting point about anti-matter was that it was theorized before it was discovered. It just naturally comes out of combining Special Relativity with Quantum Mechanics, antimatter *must* exist for both theories to be correct.

Neutrinos were also predicted before being discovered. In that case, there needed to be a particle to conserve and carry away the lepton number in weak interactions.

BTW I just discovered the AstronomyCast, so I haven't had a chance to listen to them all yet, have they mentioned Supersymmetry yet? That's even cooler. Each fermion/boson would have a boson/fermion superpartner. Photoninos, winos, sleptons, neutralinos, all sorts of crazy names!