Bitcoin cannot be traced
Most pool operators are known or can be determined from their spend patterns. So it would be clear to any blockchain auditor that you mined those coins.
Hence the suggestion of anonymous address-only pools. With casual usage, it is not very anonymous at all.
Transactions occur between cryptographic addresses and anyone can create any number of these addresses. However, Bitcoin transactions can be traced back to your IP address. The history of all transactions can be analyzed for spatial and temporal correlations.
As recently as 3 years ago, it seemed that anyone could buy or sell anything with Bitcoin and never be tracked, let alone busted if they broke the law. The majority of Bitcoin users are law-abiding people motivated by privacy concerns or just curiosity.
If one address can be linked to a person, then related transactions can be identified. I would say that bitcoin offers a degree of privacy not offered by other means of online payment, but for a sufficiently motivated entity, it is possible to reconstruct a person's bitcoin transaction activity.
There are steps that one can take to make it more anonymous, but it is certainly not as anonymous as physical cash. And, you have to know what you're doing to use it in complete anonymity.
I would not advise using bitcoin if you are seeking complete anonymity.