Well the definitive study to date was not able to demonstrate any efficacy for focused prayer.
Long-Awaited Medical Study Questions the Power of Prayer - New York Times
I am uncertain about the potential for prayer to work, just because their is so much about the human mind we don't understand. However, I have a tough time believing there is some God listening to each prayer and capriciously deciding which to answer. After all, if there is someone up there who allowed 6 million Jews to be killed during WW2 but can take the time to fill up someone's stove, that's someone I can't really roll with.