I find the notion of prayer rather redundant. At least going off the Abrahamic faiths whole 'God's Plan' belief. If his plan is inevitable, things will happen regardless of prayers, all the praying in the world wont change what will happen, therefore what is the point in it? The only time I see any point in it is when people are asking for guidance or forgiveness I guess, but then it leads into the argument of are they actually getting a response or just hearing what they want to hear/ formulating responses based on their own mind figuring things out one way or the other.
See to me, prayer is saying 'I am wishing really, really hard for something.. with out putting any real effort in to it'.I think to some people it may be the same as hoping or wishing about something they don't have any control over. Like if you have a beach day planned, you might really hope that it doesn't rain and ruin your day. Even someone who doesn't believe a wish on a shooting star is going to keep the rain away, I think it might give a person a little peace of mind by feeling like they have done something to make a thing they have no control over better. And with even heavier issues, like cancer or something, if every single reliable medical procedure has been tried and the outlook still looks poor, if a person even held out the slimmest belief that something like a prayer would help at all I could understand why they would, even if just to keep hope alive a little longer. I feels the same to me as setting up a dreamcatcher to keep nightmares away, or carrying around a rabbits foot to help luck stay on your side. I would doubt a person with a rabbit's foot has any more fortune than one without, but it might give them more optimism about the things that are out of their control and I don't think that's a bad thing.
Now if a person walked into a casino with their rabbit's foot and it really didn't give them luck or they greatly exaggerated the luck-swaying power of the foot I then would be worried. The weather you don't have control over - whether you put your life savings on red you do have control over. Trying every medical treatment and praying they work is doing what you can and hoping for what you can't - choosing not to get any medical treatment and believing the cancer can be prayed away is choosing not to do the thing you can control and put all your chips in the things you can't. I'm not someone who prays, but there are some situations where it would make sense to me if people do, whether it makes any difference or not.
My Girlfriend is a Pagan and believes certain rocks can help with certain things. I have a mug she gave me that I use to drink tea out of every morning, and it has a Citrine stone on the handle along with a horoscope-sounding description on a card of what it is supposed to help with. I think the idea of a stone helping to ground negative energy or help with financial prosperity is cool, but I don't put much credence in it. What it does do is make me think about all the stuff on the card which leads to me taking real action that could result in them. I may hold the stone a little tighter after applying to a new job, but at the end of the day I know most, if not all, comes more down to me and the action I take. And I just imagine a lot of people who pray feel the same. Sure, they probably take it more seriously than I do a stone on my mug, but the things they are able to do is what they focus on most, with the prayer being the little stone that might help the uncontrollables a little bit.
This post is longer than I wanted already, but just a quick aside to the forgiveness/guidance thing - I wouldn't think most people really think they get responses. At best most I think would believe God helps them find the solution or forgive themselves. Praying in a lot of ways is similar to things like therapy, meditation, or reflection just with the whole focus on some greater thing listening. Maybe the best example is a therapy bird, if you go to one with your problems its not going to tell you any answer directly, but a lot of people seem to leave feeling better and knowing what to do. The bird did nothing, but just feeling like someone was listening helped work out the problem. I think the right thing to do just becomes more obvious sometimes when another person (...or bird) is perceived to be listening.
See to me, prayer is saying 'I am wishing really, really hard for something.. with out putting any real effort in to it'.
Whether that be to find your lost car keys, find a missing child, or getting a promotion at work.