Nuclear energy usually has a significant NIMBY problem (Not In My Back Yard!) that prevents nuclear power plants from being constructed. There's no simple solution to this obstacle, and even when the reactor is going to be thousands (or millions) of miles away from any people in a spacecraft, the danger of launching a nuclear reactor on a rocket is still too risky for some folks. There haven't been any nuclear disasters in space, but as more and more nuclear powered spacecraft are built, the anti-nuclear groups may grow increasingly loud. Here are just a few nuclear spacecraft projects that could travel beyond our planet.
If you'd like to read more awesome and interesting stuff, check out this unrelated (but not entirely random!) Techdirt post