bitcoin is pseudo-anonymous.
All transactions are included in the blockchain (decentral database), so it's possible for somebody to follow these transactions (inputs, outputs, change addresses,...), and using some data mining and some clever algorithms, it's possible to find most addresses belonging to your wallets.
Couple this information with the fact that most exchanges follow KYC regulations and require your identity verification AND the fact that if you buy a physical good, you'll have to provide a delivery address. The end result is that if you ever bought bitcoin with a verified account, or spent bitcoin using your real address, somebody with enough resources and time will probably be able to find you...
That being said, no ip's are recorded in the blockchain. A node can only (potentially) record the ip of which it receives a transaction (but it can never know it is the ip of the person creating the transaction). So, if you use a VPN (or tor) and never couple a physical address or a forum nickname to your addresses, it'll be pretty hard to track you down.
There are also other sollutions to enhance your privacy, but i'm not going to go into details this time
You are right sir, That's why some of the bitcoin users here when they do transaction in withdrawal they bitmixer or chipmixer so that there transaction will not be traceable.