When I was a kid I owned a BB gun. At the time there were three ways to power the BBs:
1) A cocked spring
2) A CO2 cartridge
3) A hand pump mounted in the stock (where you pump the gun up 5 or 10 times for each shot)
Now there is a new type of BB gun called the PCP rifle. PCP stands for Pre-Charged Pneumatic. The gun has a large air reservoir and you pressurize it with a hand pump that looks like a bicycle pump. The reservoir can hold 2,000 or 3,000 PSI and can shoot many shots. You can find the guns in .177 (the usual BB/pellet caliber) and .22 caliber. This video shows you how to charge the gun:
The velocity is 800 to 1,000 feet per second, which translates into 550 to 700 MPH.
You can also get PCP air guns up to .50 caliber, and people are using them for big game hunting. This video shows you the size differences between the different calibers (turn down the volume):