The fact is you can get fairly good anonymity simply by putting your coins on an exchange that doesn't require ID, and then transferring it out to an address that you have never used.
But then you're trusting the exchange not to keep logs that link your incoming tx to the outgoing one.
right, this is why if you use an exchange that lies outside of eg. US jurisdiction, they are unlikely to comply with any requests to produce such logs.
This is likely the reason why the American/European currency authorities in particular are always vilifying the Chinese exchanges. The Chinese exchanges are a doorway in and out of Bitcoin that they don't have any control over.
-bm