Balance. If animals and people were immortal, it'd throw off the balance to everything. If evolution is correct, I'd imagine we'd NEED the birth / death cycle to be able to evolve. otherwise the same old boring strand of dna would stay the same forever, and nothing would ever change. In that case, we'd never have evolved in the first place. Who is to say that our bodies are finished evolving right now? Evolution isn't a process you can observe over even a few millenia. IMO it takes a great deal more faith to believe in a god than it does for evolution. Neither one can be explained completely or proven. How can you ask scientists to tell you exactly what happened 50,000 years ago?
The formula - 'for each action there is an equal and opposite reaction' can even be applied here. A tree living 3000 years isn't exactly going to destroy anything, is it? Why do some bugs only have a life span of hours?