Before anyone else posts a reply, please read about NERVA rocket engines, a nuclear rocket engine designed in the 60's. They used a nuclear reactor that heated up liquid hydrogen very rapidly - no oxidizer necessary - and they obtained a much greater thrust-to-weight-of-fuel ratio than chemical rockets. They were designed to be used in space, as upper stages or as what, these days, are referred to as "Earth departure stages". There was a fairly significant level of radioactivity in their reactors, but as I understand it, the level of radioactivity in the exhaust was negligible. None were ever launched, but the R&S advanced to the point where NASA could have launched these engines into space. However, the public perception of the dangers of a "nuclear rocket engine" was sufficiently negative to make launch politically prohibited, whatever the actual merits and risks associated with the design. It just goes to show you that, when it comes to politics, the facts don't really matter.
When evaluating the risks of launching nuclear rocket engines into space (or any nuclear, or otherwise hazardous, propellant and/or cargo), you should consider the fact that a number of American and Russian nuclear submarines ended up being destroyed due to accidents (or that's the Defense Department's version of things, anyway), and their reactors are at the bottom of the ocean. Huge ecological disaster? If so, then the U.S. and Russia have kept it under wraps for decades - and I don't believe that the U.S. government could keep such a big secret for so long. I am not a big pro-nukes guy, but while there are risks involved in launching such materials into orbit, they're manageable.