Chemical propellant, mainly kerosene and liquid hydrogen. These chemical reactions are used to create these massive explosions that you see in most space shuttle launches in order to achieve very high exhaust velocities, which is required to escape the Earth's gravity well and get to low-earth orbit. Chemical rockets get the job done if you want to get to low earth orbit, but they become very inefficient for anything deep space. At some point you reach a limit where you end up essentially carrying chemical propellant just to propel the propellant. This problem blows up to infinity very quickly.
The thing that excites people in the field these days is
field propulsion, which is basically propulsion without carrying any fuel on board. This circumvents the main issue associated with the Tsiolkovsky rocket equation, but the trick is to not violate the law of conservation of linear momentum (or, equivalently, Newton's third law). Some of these ideas are promising, while others are currently science fiction.