There are three proposed means of interplanetary travel which get the most attention - bipropellant liquid rockets, electric engines, most notably the ion engine or ion thruster, and the more experimental (but extremely promising) VASIMR, a variable specific impulse magnetoplasma rocket, which uses radio waves and magnetic fields to accelerate a propellant. These interplanetary propulsion systems have an exhaust velocity (i.e., top speed) of 3 - 5 km/s, 30 - 50 km/s, and 10 km/s - 300 km/s, respectively. Specific impulse (miles per gallon, basically) ranges on a similar scale. To get off the planetary surface initially, solid rocket boosters are often used.
Bipropellant rockets have been extensively used throughout the space program, and took men to the Moon as well as being used as the primary means of interplanetary travel for satellites. Ion engines are new and were only first tested in space in 1998, onboard Deep Space I. VASIMR engines are even newer and have only been tested on the ground. The first in-orbit tests are expected to take place in 2010.
Bipropellant rockets are preferable to solid rocket boosters for interplanetary maneuvers for multiple reasons, the most obvious of which is that bipropellant rockets can be turned on and off while solid rockets are a one-shot deal. They also offer an improved specific impulse and top speed. The downside is that they are more expensive than solid rockets due to the pumping machinery. Solid rockets work based on more of a "fire and forget" principle, just like bottle rockets - you ignite them, they fire, and that's it. Bipropellant rockets have many more moving parts. Yet, for interplanetary propulsion, they're usually considered standard. These rockets combine together a fuel and an oxidizer at high pressure using turbopumps to produce thrust.
Ion engines work similar to particle accelerators - they ionize some substance, usually argon, mercury or xenon, and accelerate it out a nozzle using a powerful electric field. This takes advantage of the charge-to-mass ratio of ions to produce thrust. Ion engines are exclusively for interplanetary travel because they produce far too little thrust to ascend from the Earth's gravitational field. Unlike the ion engines portrayed in Star Wars, real ion engines take many weeks or months to accelerate up to a reasonable speed, but have a very high specific impulse and top speed compared to conventional rockets, making them attractive.
VASIMR is the most advanced, but thoroughly feasible proposed interplanetary propulsion system. As stated earlier, the system uses radio waves and magnetic fields to accelerate a propellant, usually hydrogen. A magnetically-induced "choke" allows a variable nozzle stream, hence the variable specific impulse component of the acronym VASIMR. These systems show the most promise, capable of accelerating continually, and could shorten the trip to Mars from years to 8 months or so. The VASIMR was originally developed during research into nuclear fusion.
