Some ISP's offer daily I.P address renewal's. You may also be able to get some sort of I.P blocker. But...Be more specific on what you mean by "anonymous". Overall, if you have a good firewall and virus protection, and you don't giver any personal info away, you should be O.K.
But seriously if you want to stay anonymous and the above doesn't work, try using a free proxy server and only give away fake details about who you are. It would also be a good idea to use an application like Peer Guardian.