"Anonymity" is a vague phrase and we've got to be careful what kind we're talking about.  It might for example mean:

(1)  Not having your name directly on a transaction, but any competent investigator (the attacker) could talk to a merchant who has a database associating your name with certain Bitcoin address(es) and find out that your name controls those address(es). 
(2) Same as (1) but instead of finding out your name they simply geo-locate your address(es) by linking them to your IP address.
(3) Same except instead of name or geo-location they figure out what kind of business you are up to from the detailed history on the Bitcoin chain of which addresses you've transacted with and when. 
(4) They figure out all of (1)-(3).
(5) You try to avoid any of (1)-(4) by trusting intermediaries not to keep logs.
(6) Secure untraceability, which avoids (1)-(5) without having to trusted anybody in particular.   Tor, for example, can mostly achieve this (every relay in chain would have to collude or be simultaneously monitored) for individual encrypted messages.

I only call (6) _secure_ anonymity.   (1)-(5) I am uncomfortable with people advertising as "anonymous" because, although it might not have your name directly in the log, "anonymity" in the crypto community has traditionally meant something much stronger, i.e. secure untraceability.    Computers have perfect memories and are full of obscure caches, and in the financial world intermediaries are often required to keep logs by law, so you should just assume they will remember everything rather than trusting them not to.

I don't know how to make secure anonymity work directly with Bitcoin, since having the transactions be public and related (by chains, by addresses, and by signatures) is part of Bitcoin's security protocol while secure anonymity is about making each transaction unlinkable to the others.   It can be made to work indirectly by having an intermediary issue a different kind of coin, blinded digital cash, and then mixing much as suggested above.    Then if you want to be anonymous you exchange your bitcoins for anonymous cash and if you don't you just use bitcoins directly.     The issuers of anonymous cash can be required by customers to use bitcoins to keep securely auditable reserves so bitcoins would still be adding tremendous value in making the currency more trustworthy even if everybody else is using the anonymous cash instead of bitcoins directly.   This dual setup is very analogous to a bank holding gold reserves and issuing bank notes, except the "gold" in this case, bitcoins, can be made much more securely auditable and much harder to steal.   Since the anonymous cash is blinded each transaction is securely unrelated to the others and one does not have to worry about either the intermediary or the merchants keeping logs or linking your name to a particular transaction.   Because the logs can't be pieced together to link transactions to each other.   Google "blind signature"+"cash", there is a good technical literature out there about how to do securely anonymous digital cash.   I particularly recommend "double blinded" cash as it allows the payee as well as the payer to remain securely anonymous.