With onion-routing a relay in a circuit only knows its predecessor and its successor, while a "normal" proxy is just one hop, so that it knows who connects to it and where it has to connect to.
Wouldn't it be sufficient enough, from the anonymity point-of-view, to have just two hops, guard and exit? The Guard knows where the request is coming from and the exit where it is going to.
Why does Tor use three hops, instead of two?
Maybe think of it as a defense in depth idea. If you only have two hops, and your adversary owns or watched your exit node, they immediately know which other node to compromise to get you.
That single node is a particularly high-value target since you'll be using your guard node for a while, so maybe it's worth investing some resources to be able to watch that. Due to the middle hop this equation changes slightly.
Now of course the next question is "why not four"? At some point adding more nodes just increases latency and doesn't add that much security. And some attacks don't care how often and long you bounce around within the Tor cloud anyway.
It just seems that three is a good compromise, or as Roger put it "3 is a good number of anonymity".
