There are many variants of the flight altitude record. The highest on the list is SpaceShipOne but rocketry isn't really "flight" in the sense of aerodynamic lift. What is the highest altitude for which:
The flight at a reasonably constant speed and altitude "straight and level". It is not in free-fall, so the "cabin" feels about 1g.
It is "heavier-than-air" and supported by lift rather than buoyancy. The engine thrust's vertical component is much less than the weight of the aircraft, so the wings or lifting body have to support the craft.
The speed is slow enough that centrifugal effects are negligible (i.e. it is not in orbit). This is the case below about 2.5 km/s (about mach 8).
The highest on the list that may qualify is in a Mikoyan-Gurevich MiG-25 at about 36000 meters. However, it is not clear if this was at the top of a parabolic arc initiated at a lower altitude. The highest (including unmanned) that surely fulfills the above requirements is the Helios HP01 at almost 30000 meters.
Helios HP01, although very light, is a very low-power craft that only uses propellers. One would think (sc)ramjet-powered craft would win due to the high speeds needed to generate lift in such extremely rarefied air. Is this the case?