Answers have included destroying everything in your path with beam weapons, moving threatening debris with magnetic fields, or having thick shields. Each of these approaches has problems. Beam weapons aren't too good, since they'd just disperse the threat and would require fantastic amounts of energy. Magnetic fields wouldn't do anything to non-magnetic particles. Hit one big grain of sand at high speed and a ship is toast.
Shields seem to be the logical answer.
What I'm talking about is asteroids. Imagine a ship which pushes an asteroid ahead of it. And if the asteroid is big and rich enough, it could be mined as a source of material for the ship. It's the most realistic method of interplanetary travel I seen. It's not sexy, it's not glamorous, it's not maneuverable - but it is more plausible than anything else.