Yes! First, it is proper and good for us to pray for each other. Jesus, Himself, prayed for all of His present and future followers. John 17:9, “I (Jesus) pray for them (true Christians). I am not praying for the world but for those you have given me, because they are yours.” Jesus also told us to pray for our enemies. Luke 6:28, “bless those who curse you, pray for those who mistreat you.”
A wonderful example of prayer on behalf of another is shown in the imprisonment of Peter. Acts 12:3, “…constant prayer was offered to God for him by the church.” When the angel came to release him, Peter wasn’t praying for himself; he was asleep. God’s will wasn’t altered by the prayers of his brethren, but God did give those Christians a great blessing: a strengthening of their faith and joy through answered prayer.
Should we actually ask fellow Christians to pray for us? Yes. The Apostle Paul specifically asked his brethren to pray for him. Ephesians 6:19 (NIV), “Pray also for me, that whenever I speak, words may be given me so that I will fearlessly make known the mystery of the gospel.”
So then, the Lord desires the prayers of His children for He has an abundance of blessings to bestow. However, we are cautioned in James 4:3 that “you ask and do not receive, because you ask amiss….” We are always to ask in accordance with His will. Even before His crucifixion while in the Garden of Gethsemane, Jesus did not ask for His will, but God's will to be done: "not My will, but Yours, be done," Luke 22:42.
God loves to bless us. When we pray appropriately, God “…will …open you the windows of heaven, and pour you out a blessing, that there shall not be room enough to receive it,” Malachi 3:10.