Anonymity

If everyone can see that the transaction took place, why is everyone worried about anonymity? That's simple: there are insufficient controls over who may create, hold or use a wallet. Things are getting better but it's still easy to create a wallet with little or no identification or, even, with false identification. So, there is no guarantee that your "counterparty" is who he says he is. However, as crypto-currencies have become more prevalent in low-grade crime awareness of the problem has reached the general population. Those "we've got video of you abusing yourself so send us bitcoin" emails (see www.globalkyc.com) are a growing problem and will only get worse.

There are, however, increasing controls in reputable countries over who may create wallet-type applications and they are required to take measures to identify those customers who are maintaining all but the smallest accounts. In theory this will have an impact on the problem but for many reasons (which are not specifically crypto-currency related) it's more difficult to identify those bent on malfeasance than it might first appear, just as it is when ordinary bank accounts are used for similar purposes.

Further Reading: All about algorithms