Meh, prayer is just another form of meditation. And there are all sorts of non-religious people out there who feel that meditation is enough to work wonders on all sorts of things. And neither group is entirely wrong. There are some merits to the healing power of the mind, but obviously it's limited. Wishing for your severed arm back isn't going to do much.
In my youth I was professionally diagnosed with
Major Depression. The traditional methods of treatment were forced on me, but they didn't really do much. It wasn't until I voluntarily spent some time in a mental hospital that I had my breakthrough. It wasn't because of therapy or anything like that. It was just the realization that if I wanted to get better, I had to do it on my own.
I don't know if anyone here has ever experienced regimented incarceration for a length of time. It's like nothing you can fathom. I was in there for only 7 days, but it was the longest length of time I've ever experienced. It felt like at least a year. I came in voluntarily, but I couldn't leave voluntarily. And I wanted out, and I lied to do it (especially after hearing insurance had granted an extra 14 days).
Sure, I had a mental illness. But I saw others who had things way worse than me. Or, at least the same as me but they chose to deal with it in a much worse way. There was a kid who had been in there 1 month (I don't even want to know how long that felt like) and on the day of his release, they gave him a razor to clean up his face for his parents. He came out of the bathroom with bleeding forearms, giggling and smiling.
After I got out of there by completely lying and saying what they were doing was helping, I decided to truly get better the way I knew that would work for me. And it was only through personal reflection and meditation that I could do that. It wasn't prayer, but I'm no stranger to prayer. Again, the two things are not dissimilar. So can prayer have the power to heal a mental illness?
In my own, personal, firsthand experience: yes (and I'd add the caveat that it may depend on the illness as well). But it wasn't overnight. It was several years of personal work.
The better question would be "Is there a magical superbeing that can heal a mental illness?" But then, that's just picking on a certain group of people. I'm of the belief that if a person is superstitious *at all*, that if a person believes they actually are in control of their fate and destiny, that if a person believes when they perform certain actions or change their behaviour slightly it can affect the outcome of completely random events (like dicerolls, televised sporting event outcomes, etc.); then those people are in the same pot and kettle boat as the religious types.
A lot of people hate the idea that life is just a big random chaotic mess. And a lot of people have their own way of sorting it out. I don't see why some people feel the need to generalize others and rag on them for their beliefs. Let them think what they want to think. It doesn't make them inferior to you in any way. If you feel that they are inferior to you somehow, then maybe it's time to do some of your own personal reflecting and get over yourself.
Sure, some people may have differing opinions and some folks go a bit too far. And it's ok to disagree with these people. But they're still just people, trying to make sense of the chaos like everyone else.