The fastest chemical rocket ever, the Star-48 engine was built to launch satellites and was recently incorporated into the New Horizons probe, which took off in 2006. Powered by burning a mixture of ammonium perchlorate and aluminum, it boosted the Pluto-bound probe to approximately 36,000 miles per hour. New Horizons should reach Pluto and its moons by July 2015.
First Used For Propulsion 1980

Ion thrusters rely on electromagnetic effects to accelerate charged particles out the back of a spacecraft, generating propulsive force. Up to 50 times as efficient as chemical rockets, they are now primarily used for satellite station-keeping. NASA’s Deep Space 1, launched in 1998, was the first probe to use an ion engine for main propulsion. Dawn, which is currently exploring the asteroid belt, also uses one.
First Used For Propulsion 1998

Like regular sails that gather momentum from wind, solar sails rely on the momentum of sunlight. Only a handful have been tested in space so far, including the Japanese Ikaros, a private effort called LightSail, and NASA’s NanoSail-D. Scientists are working on creating lighter materials and more reliable deployment methods, both of which could boost speeds.
First Interplanetary Flight 2010

Probably the fastest propulsion system scientists could build right now, external pulsed plasma propulsion would explode hundreds of nuclear weapons behind a spacecraft. The ship would ride in front of the shock waves. The idea was first studied in the late 1940s, and, technically, it could work. But implementing it is tricky: Launching a spaceship loaded with hundreds of nuclear weapons is far from safe.
Concept Tested 1957