What is the fastest airplane?
This is a broad question. The Wikipedia page on vehicle speed records gives a nice breakdown by various categories. Some criteria are manned vs. unmanned, air-breathing vs. rocket, civilian vs. military.

The fastest manned, air-breathing aircraft was the Lockheed SR-71 Blackbird with an (unclassified) record of 2,193.2 mph on July 28, 1976.

However, some would consider the rocket-powered North American X-15 the fastest manned aircraft at 4,510 mph.

If you consider the Space Shuttle an "aircraft" during its re-entry phase, it passed Entry Interface at around 17,500 mph. This was unpowered flight though, and its speed dropped off as it entered the atmosphere.

I believe the rocket-boosted HTV-2 Falcon currently qualifies as the fastest unmanned aircraft at 13,201 mph.

The record for the fastest human-made craft of any kind is currently held by the Helios probes, at 157,078 mph. The fastest manned human-made craft was the Apollo 10 spacecraft at 24,790 mph. (Note that Apollo 10 holds the record not because it was any more or less capable than any other Apollo mission, but that its chosen moon fly-by trajectory resulted in a higher top speed relative to Earth. It could also have achieved a much higher top speed on a different trajectory had that been a goal for mission planners, but it wasn't.)

Finally, every single one of these is either military or NASA (not civilian). The fastest civilian, air-breathing aircraft were the Tupolev Tu-144 supersonic transport at 1,518 mph, and its Western counterpart, the legendary Aérospatiale-BAC Concorde, at 1,488 mph. Both are now retired. Several private organizations are developing civilian suborbital and orbital rocket-powered spacecraft; I'm not sure which is currently fastest.

And though these aren't crafts or vehicles, honorable mentions go to a 150,000 mph steel plate launched by a nuclear weapon, and to particle accelerators for propelling subatomic particles and "man-made" particle collision byproducts at ridiculously close to (99.99something percent of) the speed of light :-)