Some satellites use nuclear fuel.. they're mostly the interplanetary ones where solar would be tough, but some orbiting ones do it.
In most cases it's not a full fledged nuclear reactor, it's just nuclear material in a solid that's dense enough to heat up but not enough to melt, and a thermocouple or something to generate the electricity. No moving parts. I think I read they're robust enough to survive a reentry event and be recovered and recycled.
EDIT: These things:
http://en.wikipedia.org/wiki/Radiois...tric_generator