Two studies have shown a positive therapeutic effect of intercessory prayer (Byrd and Harris). Critiques/problems with these studies include:
The scoring system used to measure hospital course. If Harris applies Byrd’s scoring system to his data, there is not a significant difference between the prayer group and the control group. This is a problem that the authors noted. A consistent scoring system should be developed that can be applied to all studies.
Byrd made no prediction of what differences he expected in hospital course between the prayed for and not prayed for groups and offered no explanation for the differences he reported in congestive heart failure, ventilation requirements or medication use. We might assume then that the results are a consequence of errors in the study. These errors might include differences in the two groups health status before hospitalization or differences in the attending physicians treatments. For example, some physicians are more aggressive with antibiotics than others and this may account for the greater use of antibiotics in the not prayed for group. These possibilities were not explored.
Four studies have shown no therapeutic effect of intercessory prayer. Critiques/problems with these studies include:

Small sample sizes. These studies range from 18 to 95 patients versus 393 patients in Byrd's study and 990 patients in Harris' study. Smaller numbers makes it more difficult to statistically prove any effect at all. Thus, we might consider these studies “inconcluisive” rather than “no effect”.
So, does the scientific literature prove that intercessory prayer works?

No, scientific literature has not proven that remote intercessory prayer has beneficial therapeutic effects. However, it has not proven that it doesn't have beneficial therapeutic effects either. More studies would have to be done that replicate Byrd and Harris' studies using a consistent scoring system that has reproducible results.
Does it matter if we prove that intercessory prayer works or not?

No, the general population doesn't care what the scientific literature proves or does not prove. If they believe in God and the power of prayer for healing, they will continue to pray. In a recent issue of Academic Medicine, there is a letter to the editor ????ted by Dr. Brian Kavanagh in response to Dr. Edward Halperin's article "Should Academic Medical Centers Conduct Clinical Trials of the Efficacy of Intercessory Prayer?" Dr. Kavanagh concludes:
"In the final analysis, everyone does his or her own clinical trial of intercessory prayer internally. If praying for themselves, their loved ones, or strangers afflicted with illness provides some measure of good feeling or emotional relief in stressful times, people will continue to do it."