Bitcoins are much less anonymous than normal net traffic, even. If someone sends you some money, you get to know the address it came from, and plug it in on http://blockexplorer.com/ and you can see which addresses that address got its money from, and how much, and you can trace it all the way back through history to find out which block generated the money and how it got to that address. Depending on how people consolidate their wallets, you can even see how much money they have.

I don't have to be routing packets for you to find all this out; every transaction goes to every node.

There are "laundering" services which try to play a shell game with addresses, but I think they're probably easy to reverse-engineer, at least probabilistically if not completely.

OTOH, unlike IPs, you can't pinpoint addresses to any location though or find out who owns what addresses for sure. I guess they're more pseudonymous than anonymous.