Studies have been done on the positive effects of prayer on health and recovery, and I'm sure someone here can point us to information on the web. My guess is that such studies are not scientifically valid because they would need to be double-blind where the patient doesn't know if he's being prayed for or who is praying for him, and the person doing the praying doesn't know which patient they're praying for, if any.
Naturally you couldn't have a blind study where the patient prays for himself. I suppose you could have a comparative study, though, where they measure the relative success rates of praying Catholics against praying Baptists and so forth.
--Percy