I'm not Christian but I've never found it a problem if people want to pray for me. Nice to know that they care for me, and are thinking about me. And believe me, that was a good thing to know a few years back. Sometimes like anything else it can be nice to share a problem, and I think that in that sense at least prayer works - can help people to de-stress by "sharing" their problem with their God.
Of course, as even my Christian Mum has pointed out, if you pray for someone who is sick and they get better, that's almost certainly down to the doctor or surgeon (although maybe "God was acting through him" - or not, if the operation failed). But I think most Christians I know are sensible enough to know that if they want to sovle problems, they have to DO things themselves. It's just that praying beforehand, and focusing on the problem, thinking about it, sharing it, can help them to be able to do that.