Christians have always prayed each other since the beginning. We see this in the Bible:
About that time Herod the king laid violent hands upon some who belonged to the church. He killed James the brother of John with the sword; and when he saw that it pleased the Jews, he proceeded to arrest Peter also. This was during the days of Unleavened Bread. And when he had seized him, he put him in prison, and delivered him to four squads of soldiers to guard him, intending after the Passover to bring him out to the people. So Peter was kept in prison; but earnest prayer for him was made to God by the church.
(Acts 12:1-5 RSV)
I appeal to you, brethren, by our Lord Jesus Christ and by the love of the Spirit, to strive together with me in your prayers to God on my behalf, that I may be delivered from the unbelievers in Judea, and that my service for Jerusalem may be acceptable to the saints, so that by God's will I may come to you with joy and be refreshed in your company.
(Romans 15:30-32 RSV)
You also must help us by prayer, so that many will give thanks on our behalf for the blessing granted us in answer to many prayers.
(2 Corinthians 1:11 RSV)
Pray at all times in the Spirit, with all prayer and supplication. To that end keep alert with all perseverance, making supplication for all the saints, and also for me, that utterance may be given me in opening my mouth boldly to proclaim the mystery of the gospel, for which I am an ambassador in chains; that I may declare it boldly, as I ought to speak.
(Ephesians 6:18-20 RSV)
Continue steadfastly in prayer, being watchful in it with thanksgiving; and pray for us also, that God may open to us a door for the word, to declare the mystery of Christ, on account of which I am in prison, that I may make it clear, as I ought to speak.
(Colossians 4:2-4 RSV)
Brethren, pray for us.
(1 Thessalonians 5:25 RSV)
Finally, brethren, pray for us, that the word of the Lord may speed on and triumph, as it did among you, and that we may be delivered from wicked and evil men; for not all have faith.
(2 Thessalonians 3:1-2 RSV)
First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all men, for kings and all who are in high positions, that we may lead a quiet and peaceable life, godly and respectful in every way.
(1 Timothy 2:1-2 RSV)
Pray for us, for we are sure that we have a clear conscience, desiring to act honorably in all things.
(Hebrews 13:18 RSV)
Indeed, Jesus said that wherever two or three are gathered in His name, there He is with them.
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."
(Matthew 18:19-20 RSV)