You can put your bitcoins into an online wallet like MyBitcoin https://www.mybitcoin.com/ https://www.mybitcoin.com/ , or an online marketplace like MtGox http:

You can put your bitcoins into an online wallet like MyBitcoin https://www.mybitcoin.com/ https://www.mybitcoin.com/ , or an online marketplace like MtGox http://mtgox.com/ http://mtgox.com/ , and then send them back to yourself at a new address. As long as the service has a large enough pool of coins and enough transactions (MtGox almost certainly does, MyBitcoin might but I'm not sure) and you don't do anything dumb like always transferring chunks of exactly the same amount in and out in a predictable pattern, it will be pretty much impossible to connect the transactions, so you'll now have completely anonymized money at a new address. Of course, if you do this to cover up illegal activity and get caught at it (someone searches your computer and finds the private keys for both sides of the transaction) then you could probably be prosecuted for money laundering as well, so I don't necessarily recommend it. But achieving anonymity is not all that hard as long as you pass the money through a large third-party pool somehow.