There are many wonderful things that happen by means of prayer. The greatest effect, of course, is that God is glorified. Jesus instructed us to pray, "Father in heaven, hallowed be your name" (Matthew 6:9). That is the deepest goal from which every other prayer is extrapolated. God has ordained the prayers of his people to be the way through which he accomplishes "the victory of Jesus over this world" -- and when we pray unto this end, with God's glory as our goal, he literally takes up our feeble requests as the avenue through which he does amazing things. And that is enough for us.
But there are many wonderful things that happen by prayer, and another aspect is the effect prayer has on us personally. There is the content of our prayers and the work of God through them, and then there is the sheer testimony to our souls that we pray. It's the witness to our person that, in the moment of prayer, we comprehend the paralysis of self-sufficiency. We intentionally look away from ourselves, empty as we are, to God, the one who has no needs.
[Read the rest of the article at Desiring God.]