I'm confounded by this stuff (i.e. religion's value in treating psychological problems) when it is used as an argument in favor of religion.
Charismatic Evangelical churches teach people that the creator or the universe is madly in love with them. It tells them they have a unique and special purpose. It tells them they are no longer accountable for their previous mistakes and misdeeds because God provided a means for them to be forgiven and be cleansed "white as snow". It tells them "perfect justice" will be doled out by their perfect "heavenly father" so that all their enemies will be punsihed and they will reap rewards including a mansion in eternal paradise where there is no pain or hunger or sickness or anxiety or depression.
If you can people to believe this stuff—that God is on their side provided they meet a few simple criteria—then they are going to be markedly happier. I'd also posit it could help many with specific depressive and anxious tendencies—the type that lead to many psychological diagnoses of "mental illnes".
So, yes. Obviously "religion" can help. It can be very pyschologically sustaining. So can lots of falsehoods.
I get papers cited at me, (the first is about "religion and spirituality", the rest about specific meditation disciplines) about but I can't tell whether they're well-done or not. I believe LessWrong is the ideal place to ask about this because there's a healthy combination of interest for self-improvement techniques and solid skepticism against quackery. I thought it would be a solid enough topic to merit its own thread rather than a discussion in Open Thread.