Bitcoin
can be anonymous. All you have to do is mine the coins while you are on an anonymous internet connection (such as tor and a public wifi hotspot).
Another way for bitcoins to be anonymous is to use a "mixer". If you send your coins to a very large wallet (that contains a lot of money owned by a lot of other people), and then whoever controls that wallet then distributes those coins to a bunch of other newly created addresses (which you control the keys for), then there would be no way to tell whose money was sent to those wallets. It might be your money. It might be a thousand other people's money. This is called bitcoin laundering.
Transactions are always traceable, though. People might think their bitcoins are safe and anonymous, but then they use their own personal computer on their own personal internet connection to actually spend the bitcoins on something illegal. Guess what? News flash! The NSA and who knows how many other government agencies have been monitoring internet traffic since the 90s! Ever heard of Carnivore? How about NarusInsight? Do you honestly think they can't track P2P traffic? Do you honestly think that your P2P bitcoin spending transaction can't be traced back to your IP and to your address? They can probably track a lot of Tor traffic, too.
The only way bitcoin is anonymous is if someone keeps every single step of the entire process anonymous. Mining/purchasing has to be anonymous. Storage has to be anonymous (no third party wallets). Using an exchange has to be anonymous (good luck with that). Selling the coin (or purchasing something with it) has to be anonymous. The chain is only as strong as its weakest link, and each link has many potential attack vectors.
For example, you might think you are using a perfectly safe bitcoin "mixer" service, but for all you know, the feds are actually the ones operating the mixer service, and are tracing every single transaction from start to end.
So yeah. The long and short of it is that Bitcoin is heavily monitored and traced, which is why the government allows it to exist.