Bitcoin isn't inherently anonymous, but neither is TCP. However, that doesn't mean you can't send data anonymously over the internet through services like Tor, and the same applies to bitcoin.
Bitcoin can be made anonymous by swapping coins of equivalent value between accounts; as there's nothing that connects an account to a person, you can muddy the waters enough so that it's impossible to know which coins belong to you.
It takes some effort to make the laundering believable, especially if you use an exchange to get your bitcoins (which most do).
I think that online laundry services have the potential to be much more effective than an individual operator in most cases, but then you have to decide if you trust btc mixers/launderers and most of them charge a significant fee.
Bitcoin can be made anonymous by swapping coins of equivalent value between accounts; as there's nothing that connects an account to a person, you can muddy the waters enough so that it's impossible to know which coins belong to you.