Hello.That's a good question. It's a technical area and more people assume it is anonymous than should.The straight answer is that there are no IP addresses stored on the blockchain. But not so fast!The more complicated answer is that a node on the bitcoin network such as your client doesn't know if another node is passing on a transaction from a different node, or whether that node created the transaction itself.However, it is not that simple either. Example: if you signed up with mtGox, giving your real identity etc, and transferred bitcoin to your wallet address, and then used that same wallet address thereafter, then you have lost your anonymity. An investigator can just look and see that MtGox sent you bitcoins, obtain your identity from them, and then examine the transactions you made thereafter. If one of them is linked to illegal activity, then that's going to be problem for you.That is why it is mandatory to always use One Time Only B$ addresses. Never use an address >1 time.Finally, some deanonymizing attack is always a possibility, so just route your B$ traffic through a proxy to be on the safe side. It is possible to torify a bitcoin client, but I'm not sure if it can depend on what client you have or what OS.Anyway, I obviously encourage more people to jump in and point out any flaws in my statements or better yet suggest improvements in simplicity/security for securing genuine anonymity with bitcoin.