For years I have held a strong dislike for the invitation at the end of a worship service. It all began when my Father-in-law (my pastor at the time) began to question the wisdom in holding an invitation as the last element of the service. He reasoned that 1) most of the time no one came forward, 2) when no one comes forward, the service feels subconciously like a failure, so 3) most of our services become downers for the congregation, giving us less faith in our church.
I wholeheartedly agreed with this logic at the time, and I still think that it holds up. In the years since then, though, I have noticed another problem with the invitation. We understand from Scripture that "no one comes to [Christ] unless the Father draws him" (John 6:44). We also understand from John 6 that "all that the Father gives to [Christ] will come to [him]" and that "the one who comes to [him] will never be cast out." All of that seems to present a picture of a person saved by Christ who will come to him no matter what. The invitation, on the other hand, seems to indicate that the Spirit's drawing will be missed if not acted upon during the two verses of "Just As I Am" sung after the preaching. It is very much "man-centered" and puts most of the weight on the hearer's willingness to stand up and walk to the front.
I have often stood in the pulpit laying the groundwork for the invitation, trying to give appropriate instructions for how and why to come forward. I have also heard many other preachers do the same. What I notice, however, if there is not some kind of psychological manipulation going on ("every head bowed, every eye closed, no one looking around", etc.), is that no one comes forward during the invitation unless they have already had a lengthy chat with the pastor about salvation prior to the service and he gave them instructions to come forward during the invitation.
It seems to me, then, that the invitation is completely useless in Christian worship. When people are under the conviction of the Holy Spirit, they go to the pastor during the week or talk to one of their Christian friends who leads them to Christ. Then, once their conversion is confirmed by the pastor, they are told to walk forward during the invitation hymn and let everyone else know. Thus, the invitation system is perpetuated though it played absolutely no role in the person's salvation.
I think that a more helpful and worshipful way to end a worship service would be with...well, worship. We could sing one or two more songs and maybe partake in the Lord's Supper. Dropping the invitation would remove the misconception from the minds of the members that the only reason we are in church is so that somebody can get saved. It would remove the misconception that evangelism means inviting someone to church. It would encourage the pastor and the members to really pursue and talk to the visitors, trying to discern whether or not they are believers, prepared to witness if need be, instead of simply assuming that they are already believers or else not interested because they did not respond to the invitation.
I highly reccommend the small booklet, The Invitation System, by Iain H. Murray. He examines some of the real problems with the invitation system as popularized by Billy Graham and explains why such a thing is unscriptural.