pretty easy to get bitcoins anonymously, especially if you're the least bit creative.
Most Bitcoin exchanges only require an email and password to signup and start buying/selling bitcoins. You can use a new email address not connected to you, for example, by signing up at hushmail.com. If you're really paranoid do everything over the Tor network to obscure your IP address too.
Same thing with localbitcoins.com. All they ask for to register is an email address and password.
The entire Bitcoin community, including the new businesses/exchanges now supporting it are aware of the strengths of Bitcoin, namely in providing payment freedom and anonymity when possible. You'll find most try to make your life easier for that.
Also, if you do happen to buy bitcoins traceable to you that you want to "disconnect" for whatever reason, you can use a mixing service.