BitCoin is no more anonymous than your IP address. As soon as your BitCoin address can be tied to your identity, such as by trading through a major exchange, your transactions might as well have your name on them.

Like IP, anonymity can be emulated through routing mechanisms. Basically laundering your packets and coins. Tor, the state of the art in this kind of anonymity, is not without faults. And there isn't really an equivalent to Tor for BitCoins that I know about.

Related, I know BitCoin can be run over Tor, but this is not the same as a Tor for BitCoin. This merely protects against traffic analysis to tie your BitCoin account to your IP address.

Tor for BitCoin might look more like a network of wallets that simulated a perfectly noisy economy. If A wanted to pay B, A's coins would go everywhere to B, C, D, E, F and so on. Over time coins would pass in and out of people's wallets until at some point the right number would stick to B's wallet equal to the number A sent. Hopefully, the ones that stick to B's wallet will be a mix of ones that A actually sent and other coins being anonymized by the network.

There are obvious flaws in this design. But hopefully it helps illustrate why BitCoin isn't anonymous and the difficulty of making it anonymous.

This is certainly key to the appeal to the current enthusiasts, but (to pick an obvious example) suitcases full of dollar bills or Krugerrands are also decentralized and anonymous, compared with centralized and usually non-anonymous methods such as credit card transactions or bank transfers. Most people don't find these other decentralized and mostly anonymous currencies to be especially interesting unless they are engaged in illicit activities or traveling to places where the banking system cannot be relied upon.

I expect the actual appeal is that the value is these attributes in common with the fact that it is virtualized -- i.e. the value resides in data rather than in a physical object such as dollar bills or gold. With data, you don't have something tangible that you have to smuggle across a border in person, you just store it safe somewhere and retrieve it over a secure computer connection wherever you need it.

Or alternatively, you could use bitcoins to purchase something else virtual anonymously. (If you use it to purchase something physical, than there is an audit trail attached to the transference of the physical goods that defeats some if not all of the value of the anonymity.)

Perhaps this makes bitcoins especially useful for some scenarios, but overall I haven't yet seen any use cases that lead me to believe that this is a breakthrough of any particular kind.