I've heard that airliners' tires will last about 200-250 depending on how many hard landings are made. Bizjet tires will last longer, and light aircraft tires will last indefinitely, depending on how gentle you are and what kind of surface you're landing on. I had one start cracking around the wall and just looking unsafe long before the treads ever started to wear.
As for the spin-up idea, it's been proposed many many times, but generally always rejected due to weight and maintenance costs. However, now that fuel is by far the main expense in an airliner's trip, companies are looking for any way to reduce fuel burn. As it turns out, taxiing an airliner burns quite a bit of fuel. They've already started turning one engine off for long taxis, and I think that electric wheel motors will be the next big thing.
The motors have gotten light enough and strong enough that they are a now a viable option. They can be powered by the APU or by a set of batteries (which are also now becoming light enough, see the 787 when they get the kinks worked out). So when they get around to putting them on aircraft for taxiing purposes, you can bet that they'll be spun-up right before landing.