As n7bsn said, it's quite possible to use a 120v fixture with 12V bulbs of the appropriate type, at least in most cases. A few modern 120V fixtures designed for low power bulbs only might (emphasis on the might) have wiring that is too small for the current required for a bright 12V bulb, particularly an incandescent one, but even there I would not generally expect problems.
The opposite is not true; few if any 12V fixtures would be safe for use with 120V power, even if you could find 120V bulbs that fit the 12V socket styles.
A 120V incandescent bulb operating at 12V would produce no visible light, or close enough to no light to be the same thing, but would otherwise not have any problems or suffer any damage. An LED or CFL bulb would also almost certainly not produce any light at all, and there's a very small chance they could be damaged by DC current. (Assuming the cold impedance of the incandescent bulb is the same as the hot impedance, which is not the case, it would theoretically dissipate one one-hundredth of the power at 12V as it would at 120V. In practice I think it's somewhat higher as the cold impedance is lower than that at operating temperature, but still nowhere near sufficient to heat the filament sufficiently to glow appreciably.)
