It seems to me that Pascal's Wager doesn't need a short introduction for the members of this forum. I have seen the nonsense mentioned here a few times myself during my short stay. Despite being a laughable idea, I think it offers a lot of insight into human nature. Everybody who is slightly honest with themselves (in my estimate about 6 members of the forum) know that similar reasoning held them back at least a week or a year from declaring their apostasy to the cyber-world.
I ain't fond of homeopathy. I think it's complete bullshit but I won't stop anyone taking it. That would be illiberal. Just keep it to yourself and out of public policy. Also, I reserve the right to ridicule and criticise homeopathy and those who take it.
Regarding the psychology behind the placebo effect (cf pascal's wager), the answer yet again lies in evolutionary psychology. It seems we evolved this bias from our days when we had predators to fear and we couldn't afford to take any chances when we sensed danger. Those who took chances were wiped out from the gene pool.
See this nice short article on the subject:
http://aminotes.tumblr.com/post/528057588/why-do-we-believe-in-god-we-are-religious-becauseI believe in (real) medicine, tested by science, approved by hospitals. However, when I fear that I may get a cold I buy some echinacea extract and homeopathic pills that have 2X amount of active ingredient. As far as I know, 2X is another word for 'magic nothing' and the pills are made of useless water and glucose. I laugh at quackeries like religion or homeopathy if someone mentions them to me, then why do I still waste my time and money on 'natural medicine' or whatever they call it?
Similarly to Pascal's Wager, I reason that it won't hurt but it could help, so why not? Does it help - I'm not sure. Could it be psychological placebo-effect? Maybe, but so what, if it helps?
Have you tried echinacea to strengthen your immune system, despite being almost certain that it is bullshit? What about homeopathy?
To be honest, since becoming an atheist, I can't see even the placebo effect working on me. Maybe one day I will wish I could fool my brain into thinking it is being cured, if I get cancer or something -- to at least stop me from getting too depressed.