Nuclear fuel is of limited use in a rocket.
It can be used to generate electricity for the ship's systems, but it would never be able to get a ship to orbit.
Basically, nuclear propulsion (using heavy, fissile elements) is possible but so expensive, dangerous and difficult to achieve, that it will never become a viable option for spacecraft.
Pulsed fusion reactions (mini H-bomb explosions) are feasible, but again very expensive and tricky to perform, relying on very rare isotopes of Hydrogen to power the reaction. Not to mention the high-energy neutrons produced, which, being neutral, cannot be directed by magnetic fields- so the ship would need pretty massive shielding to prevent frying the crew.
Antimatter will never happen. For so many reasons. Nice thought, but no...
**Big Edit: just checked out the purported methods of nuclear rocket propulsion- would seem that a nuclear fission reactor can be used to superheat liquid hydrogen, which is then blasted out to provide thrust. Most of the methods have used hydrogen, not the heavy fissile metals, so harmful fallout is not really a problem. None of them are any good for getting off the Earth, they could be used once free of its mavity, though. Don't think any of them would be suitable for carrying crew, either...