On the one hand, bitcoin is entirely anonymous. On the other, it is completely transparent and trackable. Due to this fact, bitcoin is often cited as being pseudonymous.
This fact resulted in some companies emerging with the goal of controversially tracking suspect transactions to 'police' the blockchain. To counter this, ideas were developed in the bitcoin community to take anonymity further, such as merge avoidance, stealth addresses, and coin mixing.
The alpha version of Dark Wallet – a crowdfunded bitcoin wallet – went live in May 2014. Created by Amir Taaki and Cody Wilson, Dark Wallet was designed to provide new tools for financial privacy, including in-built coin mixing and stealth wallet addresses. At the time of writing, the developers are urging users to use the testnet with 'play money' to iron out bugs before risking significant amounts of bitcoin.
Wallets and services like Dark Wallet ultimately mean that using bitcoin can be as anonymous as you want it to be.