I have always thought of prayer as much more than just asking god for favours - several phrases from the bible have meaning for me, but that does not mean I believe in any god. I often say to myself, when I am contemplating some of my marvellous mountain scenery 'Be still, and know that I am god'. The 'being still' part makes sense to me, whoever said it. I think many people are too busy rushing around, trying to fit too many things into their lives, so they have no time for quiet contemplation.
I accept that praying might be one way to give people the chance to slow down and just be.
Of course, there is also the placebo effect, but I remember a surprising piece of research (sorry, I can't remember the provenance) which found that people who knew they were being prayed for actually felt stressed because they felt they 'owed' it to the people praying to get better.
All in all, I think praying, for whatever reason, might be helpful to believers and can do no harm. However, I am thinking of private meditation, rather than the somewhat boring repetition of standard prayers.