As discussed in the past religion can provide placebo benefits but this has nothing to do with the supernatural. The New York Times confirms this by pointing out that secretly praying for someone with an illness doesn't help. See also here.
This is research with serious intent. While it is important to understand the functional consequences of religious faith, research on the effectiveness of silent prayer is foolish.
Update: There is a discussion on this over at Crooked Timber which provides the abstract to the specific study. The best of the comments sites a study by Francis Galton in 1872 which rejected any beneficial effects on the object of prayer but which recognised a 'reverse placebo' effect that can comfort the person praying - prayer as a literate cry for help:
'Nothing that I have said negatives the fact that the mind may be relieved by the utterance of prayer. The impulse to pour out the feelings in sound is not peculiar to man. Any mother that has lost her young, and wanders about moning and looking piteously for sympathy, possesses much of that which prompts men to pray in articulate words. There is a yearning of the heart, a craving for help, it knows not where, certainly from no source that it sees. Of a similar kind is the bitter cry of the hare, when the greyhound is almost upon her; she abandons hope through her own efforts and screams,—but to whom? It is a voice convulsively sent out into space, whose utterance is a physical relief. These feelings of distress and of terror are simple, and an inarticulate cry suffices to give vent to them; but the reason why man is not satisfied by uttering inarticulate cries (though sometimes they are felt to be the most appropriate) is owing to his superior intellectual powers. His memory travels back through interlacing paths, and dwells on various connected incidents; his emotions are complex, and he prays at length.'