Many studies have been done to determine whether prayer actually has any effect, but perhaps one of the most famous and thorough was done in 2006: http://www.nytimes.com/2006/03/31/health/31pray.html?pagewanted=all. It was a multi-milion dollar study which was aimed at finding out whether heart surgery patients had any better recovery if they were prayed for by several church congregations. What they found is that there really is no positive effect of prayer, which really shouldn’t be too surprising to many. Prayer is one of those things where it’s very easy to get a placebo effect, or to see a ‘sign’ in a small thing that your prayer was answered. However, when actual science and facts are involved to determine whether there is any real effect, as expected, there really isn’t any.
So the long and short of it is, if you like to pray and it makes you feel better mentally, then go ahead and do it. But if you’re expecting your prayers to deliver results, then you might be better served researching doctors and hospitals to find the best ones.