@Astrodude:
Ziggurat's point about the scattering of light is good evidence that the neutrino has zero charge (or, if you prefer, a charge so small that we cannot detect it).
David mentioned beta decay. If we're allowed to assume that local charge conservation holds (and there have been no observed violations), then the total charges on each side of the decay process
neutron --> proton + electron + electron-antineutrino
must be equal. If the sum of the electron and proton charges were not zero, then hydrogen gas would carry a net charge. Given that hydrogen is the most abundant element in the universe, the upper bound on that net charge must be truly tiny (I'm afraid I do not have the details, though).
So we're left with the charge on the neutron being equal to the charge on the antineutrino, to within very tight limits. But if the neutron carried a charge then atoms with neutrons (i.e. virtually all atoms other than hydrogen) would carry a small net charge. Consider the number of atoms in the earth alone - it should be possible to obtain an extremely low upper bound quite easily, but physical intuition already tells you it must be something incredibly tiny.
Furthermore, the particles we know to be charged (quarks, electrons, muons, ...) all carry an amount of charge equal to an integer multiple of (e/3), -e being the electron charge. For theoretical reasons, it is reasonable to disbelieve that the neutrinos' charges would be exceptional, and to believe that they are exactly zero.
In the end, the assumption of exactly neutral neutrinos is just the simplest model which is consistent with the observed facts.
Edit during preview: I just came across this paper, which you might find interesting:
http://iopscience.iop.org/1742-6596/203/1/012100/pdf/1742-6596_203_1_012100.pdf
According to that, the experimental upper bound on the neutrino charge is 10
-21 of the electron charge. The bound was obtained through reasoning similar to that which I outlined above (the observed neutrality of matter, charge conservation in beta decay, etc.).