What stops planes from being stolen?
There are a several theft-deterrent mechanisms in place.


On small airplanes, most commonly, the door to the airplane itself is usually
locked with a key. (Notice the key cylinder in this picture below the silver door handle:
Prop locks:
Throttle locks:
A lot of airplanes do have an ignition key which you turn to engage the starter.  Of course, as jaytre mentioned, this can be circumvented by hand-propping (which is a very dangerous endeavor for unskilled people who haven't done it before)
You would have to know how to operate the basic systems of the airplane as well as how to fly.
AOPA's Airport Watch Program
Fences and other physical security measures around airports.