Prayer is the act of speaking to a god or goddess, either mentally or out loud, to profess loyalty, express gratitude or ask for favors. If prayers are answered, this is evidence that God exists. If prayers are not answered, some conceptions of God cannot exist.
Prayer in Christianity
Prayer in the New Testament is presented as a positive command (Colossians 4:2 ; 1 Thessalonians 5:17 ). Christians are challenged to include prayer in their everyday life, even in the busy struggles of marriage (1 Corinthians 7:5 ) as it brings people closer to God.
Prayer in the New Testament is also presented as being completely dependable. For example:
"Ask, and it will be given you; seek, and you will find; knock, and it will be opened to you. For every one who asks receives, and he who seeks finds, and to him who knocks it will be opened. Or what man of you, if his son asks him for bread, will give him a stone? Or if he asks for a fish, will give him a serpent? If you then, who are evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him!"
"For truly, I say to you, if you have faith as a grain of mustard seed, you will say to this mountain, 'Move from here to there,' and it will move; and nothing will be impossible to you."
"I tell you the truth, if you have faith and do not doubt, not only can you do what was done to the fig tree, but also you can say to this mountain, 'Go, throw yourself into the sea,' and it will be done. If you believe, you will receive whatever you ask for in prayer."
"Therefore I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours."
"Truly, truly, I say to you, he who believes in me will also do the works that I do; and greater works than these will he do, because I go to the Father. Whatever you ask in my name, I will do it, that the Father may be glorified in the Son; if you ask anything in my name, I will do it."
"Again I say to you, if two of you agree on earth about anything they ask, it will be done for them by my Father in heaven. For where two or three are gathered in my name, there am I in the midst of them."
Thus, the stipulations one must fulfill for having their prayers answered are these:
- Have faith. It doesn't matter how much, for even someone with the faith of a mustard seed will have their prayers answered.
- Don't doubt in your faith.
- The prayer must be sincere. Moroni 10:4
- Believe in Jesus and the works that he does.
- Believe that you will receive what you pray for.
- If you really want your prayer answered, get a group of people to all pray for the same thing.
- If your prayer is not answered it.s your fault because you didn't have enough faith.
The Bible says that if you adhere to these rules then this is what God will do for you:
- He will answer your prayers, no matter what you ask for.
- Nothing will be impossible for you if you pray about it.
Can prayer move mountains?
According to Matthew 21:21 and other verses prayer can indeed move mountains.
If ye have faith, and doubt not, ye shall not only do this which is done to the fig tree, but also if ye shall say unto this mountain, Be thou removed, and be thou cast into the sea; it shall be done. 
Has this ever happened? If a mountain ever fell into the sea it would cause such an enormous tsunami that history would record it.  Any number of Christians have faith, Christians who don’t know about the tsunami might well pray in faith for a mountain to move but history does not record a mountain moving. This verse of the Bible can’t be literally true.
By the way if Jesus was an ignorant 1st Century wandering preacher we can easily understand him talking about prayer moving mountains. Those who imagine Jesus was God and was therefore omniscient must wonder why on Earth Jesus would encourage good people to pray for such a devastating tsunami? Why does God allow tsunami in any case?
Another possibility is that modern Christianity has drifted so far from what God intended that he feels under no obligation to listen to prayers.
No public prayer
The New Testament says prayer should be done in private. This is obviously incompatible with public worship and ignored by mainstream Christianity.
"But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you."
The biblical Jesus usually prayed alone, for example Mark 1:35 . Jesus does not have him spend much time in temples, or encouraging church attendance. He also rarely lead public prayer, only occasionally blessing food, but he rather focused on teaching and miracles.  Mainstream Christians downplay the verse and put all the emphasis on Matthew 6:5 which criticises prayer that is exhibitionist or self-important.  Some apologists have the double-think logic of performing private prayer in public: 
- "Private prayer, as Jesus speaks about in Matthew 6:6 are words and expressions meant only for you and Him alone. I believe what Jesus is saying here is that unless you are declaring a group hug with Him at the center, then keep your intimacy with Him, intimate and private; otherwise you are only drawing attention to yourself"
If this simple verse was actually followed by Christians, their religion would be radically different. It also goes to show any text can be interpreted to mean anything people desire. Matthew 6:6 is contradicted by 1 Timothy 2:8 which calls for prayer every where.
Similar to intercession prayer, Cargo cults are a group of practices that attempt to influence Gods to grant goods and favours on believers.
Problems with prayer
God is supposedly unchanging
The act of prayer seems a little odd for people with belief in a god who is supposed to be impassible, omniscient and omnibenevolent. Clearly an omniscient god would already be aware of your problems and know what you want. Ultimately, your request may be regarded by God as either good or evil. If it is good, then why would God not have granted your wishes already? If it is evil, then why would God ever grant your request?
"Now, you come along, and pray for something. Well suppose the thing you want isn't in God's Divine Plan? What do you want Him to do? Change His plan? Just for you? Doesn't it seem a little arrogant? It's a Divine Plan. What's the use of being God if every run-down schmuck with a two-dollar prayerbook can come along and fuck up Your Plan?"
On the other hand, the Bible describes God regretting his past decisions on several occasions e.g. Genesis 6:6 and Abraham talks God out of destroying Sodom Genesis 18:23-33 , so perhaps God does change his mind.
Billions of people pray for various things every day. Many of the prayer requests are even contradictory. For instance, in a football game, often the players and fans on both sides are praying to win. If God answers prayers, which side should He choose? The side that prays loudest?
Prayer is ineffective
"[...] little prigs and three-quarter madmen may have the conceit that the laws of nature are constantly broken for their sakes -- such an intensification of every kind of selfishness into the infinite, into the impertinent, cannot be branded with too much contempt. And yet Christianity owes its triumph to this miserable flattery of personal vanity."
- — Friedrich Nietzsche, The Will to Power
- David R. Hodge, "A Systematic Review of the Empirical Literature on Intercessory Prayer" in Research on Social Work Practice March 2007 vol. 17 no. 2 174-187 Template:Doi Article abstract Template:Webarchive Full length article
- Steven Novella, The Power of Faith and Prayer?, August 3, 2011