NASA has an interesting high-level description of potential interstellar propulsion technologies based on current science. They aren't as cool as Star Trek warp drives, but at least they're somewhat based in reality. The Project Orion concept is my favorite.
Stanislaw Ulam realized that nuclear explosions could not yet be realistically contained in a combustion chamber. Such a project did briefly exist, named Helios, but its theoretical performance was so poor that it never got beyond the drawing board.
Instead, the Orion design would have worked by dropping fission or thermonuclear explosives out the rear of a vehicle, detonating them 200 feet (60 m) out, and catching the blast with a thick steel or aluminum pusher plate.
Large multi-story high shock absorbers (pneumatic springs) were to have absorbed the impulse from the plasma wave as it hit the pusher plate, spreading the millisecond shock wave over several seconds and thus giving an acceptable ride. The long arm pistons proved one of the most difficult design features but many members of the team said that this seemed solvable. Low pressure gas bags were also used for a primary shock absorber. The two sets of shock absorption systems were tuned to different frequencies to avoid resonance.
One aspect of the proposed vessel seems counter-intuitive today; because of the force involved in the thermonuclear detonations and the need to absorb the energy without harm, large, massive vessel designs were actually more efficient. Early designs had crew compartments and storage areas that were several stories tall, as opposed to contemporary chemical rockets whose height was almost all multi-stage fuel tanks with relatively little payload.
Here's more on spacecraft propulsion.