But some things are clear and this is one of the important ones. We are called to pray for one another as an act of love and obedience. St. Paul went through ship wrecks and imprisonment, challenges of health and faith, the ardors of traveling when it was unpleasant and dangerous, frustration and loneliness.
Yet, Paul wrote to Christ followers at Corinth, “On [God] we have set our hope that he will continue to deliver us, as you help us by your prayers.”*
I've had folks say, "it helped me so much to know you were praying for me" and I'm thinking, "I don't feel like any kind of super-prayer or expert." Yet my willingness to pray and my following through with prayer, and especially when I'm asked to pray aloud for someone or to pray aloud as we hold hands, all those things have been received with such love and growing connectedness. And, having been prayed for, and over by a bunch over amazing people over the years I have experienced all that as others have offered me their love and follow through.
I have learned that when I pray for someone, especially aloud, especially over a lengthy period of time, I always enjoy a deeper connection than is common in my interactions with folks. If I undertake to pray for someone who is irritating me, the irritation abates and leaves room for an open heart for that person. That does not mean I always become their bestest buddie or find them suddenly charming, but it does mean that I can be more patient and more quickly show mercy.
So I agree with St.Paul, that prayers help when others pray for us, and I believe other's prayers help me. But I also find that my prayers for others most of all change me: makes my heart more open, my judgments less harsh, my word kinder.
I have found I am blessed by prayer in all directions!
* 2 Corinthians 1:10-11 (NIV)