Obviously bitcoin is not as anonymous as we think or else there will not be the need for bitcoin mixing services.
Only really an issue for those that buy coins from exchanges (and even then, that's assuming that the exchange is passing on your cashout addresses to the police). And Kprawn is totally right; if the tumblers themselves are being run by people who collect and pass on all the info they get from their users, it's irrelevant. Attempts have been made at designing decentralised tumbling software, but I don't think all the design problems were solved. Latest, anyone?
If you bought Bitcoin in a way where your identity isn't known, it's probably not at all necessary to use tumblers, you're as anonymous as is possible
if you're 100% that nothing about the buy gave up your identity (Bitcoin should still be used over Tor so your transactions can't be attributed to your IP)