To me prayer is a way of thinking...or not thinking. Depends on the individual.
Some seem to use prayer to focus their thoughts and draw strength over issues that worry or concern them. Others seem to do them by rote and are thinking very little as they recite an essentially meaningless mantra.
The other possibility, the one I generally use for prayer, is that I recite prayers I or others have written beforehand and I contemplate the words as I am doing so. It is not rote memorization and recitation, nor am I not thinking. Yet, I am not using prayer as a time to blurt out all my thoughts and worries and concerns.
I figure God already knows my worries and concerns. I mostly use prayer as time to do two things- to be grateful and worship God and to offer prayers for the ending of suffering of all beings. It's a shifting of gears toward contemplation. I suppose in many ways, my prayers are just an extension of meditation. I feel uncomfortable with what Christians call "intercessory" prayer because it feels like meddling with the flow of the universe, but without the thought put into magical practice. Aside from that, for myself, it feels like whining to run off a list of my concerns to God. I figure if I am consistent in my focus on living my life to the best of my ability, on helping and loving others, and on worshipping God... then whatever happens will happen and my job is to focus on being peaceful and joyful enough to find these states in all situations, rather than ask for something specific.
Either way it is a time out on normal activity and maybe useful to our overall wellbeing.
I find meditation and contemplative prayer very useful to my wellbeing. It is putting time aside to bring myself consciously into a space of gratefulness, of awareness of the many blessings of life, of unity with all beings, and of compassion. It is an opportunity to reaffirm my commitment to my own spiritual growth, my patience with what gets thrown at me, and loving other beings as myself. It is also an opportunity to focus on pathways to get there, as some prayers, like the Druid's Prayer, outline a path for opening the mind and heart.
But I do not believe prayer works independent of other action to achieve the goal. And in the religious that cite 'my prayers worked' they are seeing only chance or the fruits of their other efforts beyond prayer.
The evidence is if you are going to pray for someone do not let them know you are doing it. People that know they are being prayed for do statistically worse than those that do not.
I think that is often because when you say to someone "I'm praying for you" they think that must mean they are bad off (the studies I read were conducted with severely ill people).
I believe intercessory prayer (prayers for a particular event) work basically as magic/spells do. It's a way of focusing one's intent, which also generally focuses one's actions and heightens one's observations about opportunity. It also boosts confidence and hope, which help in many situations. Basically, I think intercessory prayer generally works through means of one's personal power over one's life, not only to further particular action, but also potentially to utilize more forcefully synchronicity.
Because of this, I think it's an entirely different activity than prayer as a form of worship and contemplation or meditation. The focus (and I think the means through which it works) is different.
