Exhaust is pretty much unavoidable, even fusion and fission reactors have reaction products to be disposed of (exhaust). The trick is generating thrust without requiring reaction mass (what you toss out in one direction to generate thrust in the opposite direction, "equal and opposite reaction"). Jet engines use reaction mass, the air that is sucked in and heated by burning fuel to increase the exhaust velocity. The only thing that doesn't really use reaction mass is a propeller, which is actually immersed in it, pushing against air or water. The only known way to generate thrust without reaction mass is with electromagnetic effects. A true space drive using known principles would either use electromagnetic or gravitational effects, such as anti-gravity (Larry Niven's 'Known Space' series of novels uses gravity polarizers for normal space maneuvers, along with hyperdrive for interstellar), also useful for inertial damping. Venturing into unknown principles would create the Holy Grail of spaceflight, the "Space Drive," as mentioned in Sir Arthur C. Clarke's Rendezvous with Rama. Basically anything that would push against the space-time continuum itself ('ether'), much like a propeller in water or air, would qualify as a space drive. Spaceflight would be soooo much easier if you didn't have to carry reaction mass for ac/deceleration everywhere you go