This notion lies behind hundreds of evangelical and fundamentalist sermons which you can hear in churches throughout this country every Sunday. It also is partly responsible for the notion of God a lot of nonreligious people reject--a cosmic tyrant who demands perfect obedience and threatens us with punishment if we don't comply.
Yet Anselm actually _never_ taught that Jesus was "punished" on our behalf. On the contrary, the debt was paid precisely so that no punishment would be necessary. Jesus' death on the cross was not a sadistic punishment exacted by an angry God, but was the culmination of his absolute obedience to God's will. It was that obedience, completed in his sacrificial death, that paid "the debt we could not owe."
For Anselm, and for Christians generally, honoring God is the highest and most joyful thing we can do. It is the most truly human and humanizing activity imaginable. This is tied to Anselm's notion of God (expressed in his "Proslogion," also in this volume). For Anselm, God is the being than which nothing greater can be imagined. This isn't primarily about an omnipotent being who can make us do things. It's about a being so unimaginably glorious that the greatest happiness anyone can know is just to be in his presence. To turn away from a being like that (knowing what we're doing, which most of us don't) is to be something less than we could be. Obviously this is a bit of a modern interpretation of Anselm, but I don't think it contradicts him.
I do think, though, that there are better ways to think about the Atonement than Anselm's. Earlier Christians had spoken of Jesus' death and resurrection primarily as a victory over death and the devil--what the baptismal vows in the Episcopal Book of Common Prayer call the "forces that corrupt and destroy the creatures of God." Anselm didn't like this notion, because he thought it limited God's power and gave the devil some sort of independent existence (and in some versions even legal "rights"). But I think that that understanding of Jesus' saving work is probably truer to the Bible and Christian tradition than Anselm's.
But even if--indeed especially if--you disagree with Anselm, he's worth reading. He and the "scholastic" theologians who followed him helped shape Christian thinking in the West for the past thousand years. They are partly responsible for the fact that Western Christians--Catholics and Protestants--think so differently from the Orthodox.