SpaceShipOne is rocket propelled. So far it hasn't beaten the altitude record set by the Apollo moon rockets! As for non-rocket propelled aircraft:

1958 -- F-104 reached 91,240 ft. (piloted, jet propelled)
1973 -- Ye-266 reached 118,867 ft (piloted, jet propelled)
1977 -- MiG-25 reached 123,524 ft. (piloted, jet propelled)
1997 -- Aerovironment Pathfinder reached 71,500 ft (unpiloted, propeller driven)
2000 -- Scaled Composites Proteus reached 63,245 ft (piloted, propeller driven)
2001 -- Aerovironment Helios reached 96,500 ft (unpiloted, propeller driven)

The RASCAL aircraft currently under development by DARPA to airlaunch microsatellite rockets might beat all of them. It will be jet propelled and piloted initially, but is intended to be unpiloted eventually to increase payload capacity at altitude. During its vertical climb (dubbed the 'Zoom Maneuver') its engines will probably cut out at around 100,000 ft, but it's Mach 3+ vertical speed developed by its four MIPCC-augmented jet engines plus afterburners is supposed to carry it higher than 200,000 ft before launching its microsat rocket and free-falling back to Earth.