The answer to this question depends heavily on what you consider qualifies as an aircraft, and that distinction changes everything. The Space Shuttle Discovery holds the record for the fastest manmade object to fly as an aircraft.
The Space Shuttle was unique in that it took off on the back of a rocket but re-entered as an aircraft. Orbital velocity is over 17,000 mph, and spacecraft such as Discovery re-enter with the majority of this velocity.
This translates to speeds of nearly Mach 25 in the atmosphere, a speed unmatched by any other aircraft. From the moment the Shuttles graze the upper edge of the atmosphere, they begin to strike an aircraft-like angle of attack to generate lift. The reason why Discovery in particular claims the record for the fastest aircraft speed is its Hubble Telescope Missions, which were the highest orbits flown by the Shuttles.
For a manned, powered aircraft flying under its own thrust, the record belongs to the North American X-15. It holds the official world record for the highest speed ever reached by a manned, powered aircraft, having flown at Mach 6.70 (4,519 mph) on the 3rd of October 1967. The X-15 set speed and altitude records in the 1960s, reaching the edge of outer space and returning with valuable data used in aircraft and spacecraft design. Pilots that flew this rocket powered beast were awarded Astronaut's Wings, and the research gained from this program helped greatly in making the Space Shuttle possible. The X-15 was launched by a B-52 and then accelerated, which leads some to argue it does not count since it did not take off on its own.
If you also consider unpiloted aircraft, the X-43 reached a speed of Mach 9.8 (12,144 km/h; 7,546 mph) using scramjet technology with rocket assist. NASA built this unmanned aircraft and the key distinction is that it was uncrewed.
For a jet-powered aircraft that could take off and land on its own and fly operational missions, the Lockheed SR-71 Blackbird is the clear answer. The SR-71 can achieve Mach 3 plus speed and still holds several official air speed records. The U.S. Air Force has never revealed the ultimate maximum speed of the SR-71, but the ease with which it re-established records when broken suggests much higher operational speeds had been achieved. None were ever shot down by enemies, which speaks to its ability to simply outrun threats during missions.