Nor am I comfortable with the term, "accept Christ." It seems to connote that the "acceptor" has some kind of choice; that he is somehow the one in control, and that God needs his permission in some way. This kind of prayer and these kinds of cliches seem to be favourites of some TV and radio evangelists.
But that's not how it works, is it? I'm not even quite comfortable with the term, "sinner's prayer," but for the sake of having to call it something, that is the term I will use. In my experience, there are three occasions upon which one may pray such a prayer, and none of them are causal to regeneration.
The first relates to my own experience. I prayed such a prayer, asking God's forgiveness for my sins, thanking Him for the sacrifice of Jesus and surrendering my life to Him, in thanks for what I realized God had already done. In other words, I believe I had already been regenerated, had my eyes opened, and received a new "heart of flesh" when I prayed that prayer. If you want to read more about that experience, you may find it in my testimony
The second is from my experience with the Alpha Course. "Nicky's prayer," as I came to call it is part of the seeking process. As God calls a person and as they respond to His call, there is a process of seeking; a sort of walking in a general direction toward the light one senses. Jesus is the light of the world, and those who respond to God's call will tend to turn towards him, while those who are determined to live their lives their own way, who prefer darkness to light (John 3:19) will turn away. The Alpha prayer, to my mind, is a sincere part of desiring to know God, and praying it does not always (I might even say, not often) mean rebirth at the exact moment it is prayed.
The prayer, as I recall, goes something like this:
Heavenly Father, I am sorry for the things I have done wrong in my life. Please forgive me. I now turn away from everything I know is wrong. Thank you that you sent your Son, Jesus, to die on the cross for me so that I could be forgiven and set free. I now receive that forgiveness. Please come into my life, fill me with Your Holy Spirit, and be with me forever. In Jesus' name and for his sake, Amen.
I have prayed this prayer with a number of people and I think it is a wonderful prayer. It is usually prayed in a complete humble manner, often in contrition. It is a prayer of promises and requests, not a prayer of, "acceptance" of God.
And the third type of occasion someone might pray a sinner's prayer? To get some obnoxious Christian off their back who is determinded to, "lead them to the Lord."