There are several records for the "fastest plane" depending on what type of aircraft you are talking about.
Manned airbreathing jet aircraft: Lockheed SR-71 Blackbird -- 3,530 km/h (2,194 mph), set in 1976
Unmanned Air-launched hypersonic scramjet: NASA X-43A --12,144 km/h (7,546 mph), set in 2004
Manned Air-launched jet aircraft (incapable of breathing air)
: North American X-15, 7,274 km/h (4,520 mph), set in 1967
As a comparison, commercial jetliners such as the Boeing 747 cruise at about 500 mph (885 km/h).