Powered by compressed air, air cannons can propel whatever fits down the barrel at astounding speeds. A basic air cannon consists of a chamber to hold a volume of compressed air, a barrel to hold the projectile, and a valve to allow the air in the chamber to enter the barrel and propel the projectile. They are sometimes known as spud guns, because potatoes are a common choice of projectile. Some spud guns are powered by a combustible fuel, but I find air-powered cannons to be safer and less of a hassle.
mark 1   2003
1" barrel, dual sprinkler valve cannon.
mark 2   2004
The monster - 2" barrel, piston valve.
mark 3   2007
'Portable' 2" barrel, piston valve cannon.
The valve is crucial to the performance of an air cannon. A valve that opens as rapidly and as widely as possible will allow the full pressure of the compressed air to act upon the projectile. Generally the best are avalanche-type valves, with a small pilot valve that opens to release a diaphragm or piston to uncover a much larger opening. Sprinkler valves fit this description; they use a small solenoid-operated piston to release fluid pressure over a diaphragm. The pressure on the other side then forces the diaphragm off its seat, creating a large opening. Piston valves work in the same way, but with a sliding piston instead of a flexible diaphragm.
The chamber and barrel are most often constructed from PVC pipe and fittings. The PVC pipe must be pressure-rated; while common solid-core Schedule 40 pipe from hardware stores is, the fittings often are not. Note that PVC pipe is not rated to hold compressed gases either, as it tends to shatter upon impact and can lose strength unpredictably with age and temperature changes. Nonetheless, PVC pipe is readily available and works quite well in air cannons if properly used. The chamber and barrel should have a proper ratio of volumes. Too large a chamber will result in most of the energy of the compressed air being wasted, too small and the chamber will not have enough air to push the projectile the entire way out of the barrel. It is generally much easier to have too large a chamber than too small. I find that a chamber with between 1-2x the volume of the barrel is most effective.
Obviously these devices can be quite dangerous; if you wish to build or operate your own, you do so at your own risk.