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It's hard to say. Officially, the fastest jet plane ever built is the SR-71 Blackbird, built by Lockheed. It was capable of speeds in excess of 3.5 mach (more than 2,200 miles per hour). It was decommissioned in 1998.
The X-15 is powered by a rocket engine, however, so it is technically half-rocket, arguably eliminating it from being called the fastest airplane in the world. Falcon HTV-2. The U.S. Defense Advanced Research Projects Agency (DARPA) has tested an unmanned hypersonic glider that could be considered the fastest airplane in the world.