Here's a link to a Cochrane review of studies into whether prayer affects health outcomes. It's not a subscription site, so you should be able to read it without being on your hospital or school network. But if anybody has any trouble linking to it, I've pasted in the "plain language summary."
"Intercessory prayer is one of the oldest and most common interventions used with the intention of alleviating illness and promoting good health. It is practised by many faiths and involves a person or group setting time aside to petition God (or a god) on behalf of another who is in some kind of need. This review examines whether there is a difference in outcome for people who are prayed for by name whilst ill, or recovering from an illness or operation, and those who are not. Both groups of people still received their usual treatment for their illness. Ten trials were found which randomised a total of 7807 people. The majority of these compared prayer (for someone to become well) plus treatment as usual with treatment as usual without prayer. One trial had two prayer groups, comparing participants who knew they were being prayed for with those who did not. Another trial prayed retroactively, randomising people a month to 6 years after they were admitted to hospital. Each trial had people with different illnesses. These included leukaemia, heart problems, blood infection, alcohol abuse and psychological or rheumatic disease. In one trial people were judged to be at high or low risk of death and placed in relevant groups.
Overall, there was no significant difference in recovery from illness or death between those prayed for and those not prayed for. In the trials that measured post-operative or other complications, indeterminate and bad outcomes, or readmission to hospital, no significant differences between groups were also found. However, in the trial that differentiated between high or low risk of death, people at high risk of death were significantly more likely to live if prayed for. Specific complications (cardiac arrest, major surgery before discharge, need for a monitoring catheter in the heart) were significantly more likely to occur among those in the group not receiving prayer. Finally, when comparing those who knew about being prayed for with those who did not, there were fewer post-operative complications in those who had no knowledge of being prayed for.
The authors conclude that due to various limitations in the trials included in this review (such as unclear randomising procedures and the reporting of many different outcomes and illnesses) it is only possible to state that intercessory prayer is neither significantly beneficial nor harmful for those who are sick. Further studies which are better designed and reported would be necessary to draw firmer conclusions."