There've been some real, published studies claiming that prayer can heal people. The experiment went like this: one group was prayed for very hard by family and friends to recover; the other group received no prayer. The first group did better than the second.
From a scientific standpoint, this experiment is missing one thing:
Group 3: Family and friends pray very hard that the patient does not recover.
I do postdoctoral cancer research at a private university and have a side interest in skepticism, especially where it concerns religion, evolution, and existentialism. I'm also a Bears fan. Go Bears!