No, it is not. The ledger is transparent and everyone can keep the record of ALL transactions. It is almost possible to stay anonymous as long as nobody knows that Person X is using Address Y. Mixers are not anonymous, but they are used mostly to make it harder for someone to track you. This means that they can still track you but it is harder. However, proceed with caution. There have been a number of mixers that were scams.
You personally can remain anon. For example nobody knows who satoshi really is but they can see a lot of his transactions but can't trace them to his real world identity. You can also use mixers to mask where your coins are going.