This will be a similar post to the one I did the other day on the Psalms. I will give the reference, and then do my best to say who was praying, and the reason they were praying. I encourage you to take some time to study these. (This obviously does not include every mention of prayer).
Jesus was giving an excellent example of how to pray.
Jesus prayed the night he was betrayed. He was praying that the Father's will be done.
Another telling of Jesus' time in prayer the night he was betrayed.
Jesus set an example of prayer for his disciples. This is similar to Matthew 6:5-15.
Jesus prayed hard on the night he was betrayed. It says that his sweat was like drops of blood.
Jesus prayed for himself, then for his disciples, and finally for all believers. This is the longest recorded prayer he prayed.
The Early Church prayed the God would show his miraculous power and enable them, so that they could continue to share the Gospel with others.
Paul thanked God for the believers in the city of Ephesus. He prays that they will understand the power and majesty of who God is so they can know him better.
Another prayer from Paul. He prays that they will have Spiritual Strength. I personally memorized this a few years ago.
Paul also thanked God for the believers in the city of Philippi. His prayer was that their love for God would abound, and that they would be able to discern what is right.
Paul was thankful for the believers in Colosse. So he thanked God for them! He also prayed that they would be filled with knowledge of God's spiritual wisdom, and understanding.
2 Thessalonians 1:3-12
Paul wrote this to the believers in Thessalonica. Now you may wonder why I'm including the portion of thanksgiving, and not just the prayer. It is important to remember to praise/thank God for what he is doing. Paul's prayer was that God would make them worth of their calling.
2 Thessalonians 3:1-5
This time Paul asks for prayer. Prayer for protection, and that the word of the Lord would be spread!
Paul thanks God for what he hears of Philemon's faith. He prays that Philemon will continue to be active in sharing his faith.
Prayer is poignant and powerful. I pray that you will take the time to read these prayers. And maybe take the time to study prayer in the New Testament on your own. God's word is so powerful. When we take the time to study it, especially like the topic of prayer, it can change us.