Most of the time in this blog we pray for ourselves to become better followers of Christ. I think that is the most easily answered prayer. When we pray for ourselves we know that we are doing this of our own free will and we really desire to have that prayer answered. When praying for someone else, we may not know where they stand on the issue about which we are praying. Take for example, praying for someone to be healed of a physical ailment. If we know that the person truly wants healing then we are not praying against that person's free will. But if the person does not want to be healed what would be the point of our prayer? Do we want to ask God to heal the person in spite of what that person wants? And would God do that?
When we want to intercede for someone, it might be best to find out what the person in need really desires. If we can agree with that, a mighty prayer can be offered. "Again, I tell you that if two of you on earth agree about anything you ask for, it will be done for you by my Father in heaven. For where two or three come together in my name, there am I with them" (Matthew 18:19-20).
I think the catch is finding two or more people who really agree in prayer. At times when a group has prayed for one particular person, I have asked the individuals in the group afterward "What specifically did you pray?" It turned out that none of them prayed for the same thing. There was no agreement in prayer.