This is a great question and one that is very important. In light of this, let me give you a few important points.
First, more and more people in the world are becoming religious, apart from what people think. The rise of conservative religions is increasing, which is somewhat surprising in light of the fact that most scholars assumed that religious beliefs would be in the decline with the progression of science and human knowledge.
Second, prayer is something that most, if not all religions, believe in. They give many reasons for the need for prayer. Some say that prayer changes the heart of God. So, we ought to pray to get our prayers answered. Other say that prayer more than anything else changes the way we think. So, there is a more personal effect. Still others say that prayer is therapeutic and helps people clear their minds as they spend time with transcendent realities. In the end, there is no one reason why we should prayer.
Finally, all prayer takes faith. A person who prays must have faith that God exists and hears our prayers. Here is what the New Testament says:
"And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him." Hebrews 11:6
I will add a few links on the importance of prayer from a Christian perspective.
many people pray to god for different reasons. some to ask for forgiveness for their sin, others to ask for hope in a time of need, and some pray for thank fullness of good news or good life. whatever your need may be, god will always be there for you. sometimes it may seem as though your prayer will never get answered but just know that god always has a plan for you and all we have to do is trust him. we may not understand at the time but his intentions are always good. when bad things come our way we tend to blame god for them and our hearts turn cold as we turn away from him. but sometimes the lord does things for reasons we will never understand or comprehend. maybe there is a lesson to be learned or maybe what seems as a bad situation is actually luck compared to what could have happened. all i know is that with prayer comes a power that is greater than us and almost gives us life and hope. I am not sure where you are with your walk with god right know, that is something only you and god know; but if i am certain about one thing in life it is that there is a god. as a matter of fact there is a perfect god who is just and holy and righteous and he loves you and everyone on this earth unconditionally whether they know it or not.
I do not think that there is a different perspective in any other Divine religion than that mentioned by Readerofbooks an answer 1. Muslims have a similar perspective as given below:
And when My servants ask thee about Me, "Lo! I am surely near." I respond to the call of the caller when he calls Me. Then should they respond to Me, and believe in Me, so they may proceed aright. Quran 2:186
And says your Lord: "Call upon Me. I will respond to you." Surely those who are too prud to serve Me shall soon enter hell, disgraced. Quran 40:60
Pray provides reassurance and strength to the servants of God and that's the reason why we must pray. He surely listens, responds and leads us to the right path to be successful here and in the hereafter.