As FlyerJosh said, it depends on the aircraft. Generally, the higher the touchdown speed and the rougher the landing surface, and the higher the tire pressure, the faster they will wear-out.
High speeds are obvious: in a fraction of a second, a tire which was stationary must be spun-up to landing speed. (And why the first 3000 feet of big runways are covered with rubber deposits).
Guys flying light airplanes off of dirt or grass may have tires that last longer---the lower coefficient of friction means it takes more time to spin-up the tire, and less rubber is lost.
In jets, particularly fighters (where tires must be kept small for weight and/or space reasons), the pressure must be high: a small amount of rubber on the pavement (the tire "footprint") must do all the work of holding up the airplane. That means you need high pressures. The B-58 had main tires with 400psi. The F-4 and T-38 are 265 psi (Navy F-4s were 400 psi, I believe, when working on the carrier; 265 for land-based ops).
But it also means that during tire spin-up, that tiny little piece of "footprint" gets all the wear.
In light airplanes, I would guess tires can last 200 or more landings. When I flew the Lear 35, about 200. Airliners? Not sure, but they seemed to last a long time...maybe 200.
The T-38 I fly now: 25-40, and that is going through all the tread down through 3 layers of cord. (It has 14).
I'm pretty sure the Space Shuttle uses them once.
