The question: Does Zacchaeus repent?
Yes! No? Yes. No. Yes? No! What are we digging at? In the passage itself there is no indication that Zacchaeus meets the 'standards' of 'typical' conversion, which is more than simple historical gloss. If the scene were written with the purpose of showing a commitment to Jesus, and it is, then it would be rather odd to omit the actual conversion. Unless it is not omitted.
One detail this is often remembered about the Zacchaeus story is that he chose to give half of his possessions to the poor, along with four times the amount that he has cheated. What we have assumed is that this is the outcome of his conversion experience. What Luke is trying to show us is that this is the conversion experience. Throughout the Gospel there is a connection between those whose faith is serious and their willingness to give away their resources.
I once heard Craig Blomberg ask of this passage, "Does Zacchaeus repent? Or does Zacchaeus enter the kingdom?" The emphasis shifts away from the reception of personal religious experience to the stewardship and giving of one's self for the gospel. So the reasons why we learned this song as children don't quite hold up the same way, for we placed it in an evangelical context of inward salvation. Jesus is not willing to be confined to such a context, for his heart is so greatly driven to seek and save those who are lost that he will go wherever is necessary to bring the kingdom in all its fullness.
All of this happens with the circulating criticisms of those who can only judge the external. This is the way gospel comes into the world, with all of the whispers and grumblings designed to intimidate and embarrass. None of this external concerns Jesus when he is engaged with matters of the heart. That other stuff will have to wait until later.
Are we interested in building churches or working for the kingdom? How do we respond and welcome those who are on the fringes of the Christian faith? Is our salvation secure enough to allow God to work in ways that we previously could not imagine? Are we willing to allow the Spirit to go beyond ourselves and allow salvation to come to those in ways that are not 'evangelical' (or even 'Christian'), but which make children of Abraham?
Endnote: In a world where our most vigorous discussion swirls around trying to determine who God is going to let into heaven - and when and where and how - is it not sadly interesting that when we see a clear example of salvation (from the agent of salvation) we aren't certain how it fits into our worldview? But then again, as Rich said, We are not as strong as we think we are . . .