Blockchain transactions that use public ledgers, such as Bitcoin, are not truly anonymous. It is possible to link an address to an individual and expose all the historical transactions.
Now a recent article in MIT Tech Review has described how blockchains can be combine with zero-knowledge proofs so transactions can be provable, but truly anonymous. Zero-knowledge technology allows someone to prove that something is true (such as the fact that your have reached the legal drinking age) without revealing any information about yourself.
A truly anonymous block chain may be a game-changer for private transactions.