News this week is of Liberty Reserve, a global online currency exchange, which got shut down and its owner arrested for money laundering because it allowed sending money anonymously. Now personally I have trouble believing that every single dollar at Liberty Reserve was of criminal origin and used only to buy criminal goods. You can't "launder" money in a system which doesn't contain clean money as well as dirty one. But it is certainly true that a part of the money was dirty.
That could also have consequences for other anonymous online currencies, like Bitcoins. Basically anonymous online money has been declared to be illegal by itself, because it "could" be used for illegal activities.
Even if you don't do anything illegal, you are likely to cultivate a different image in different social circles. The quintessence of a private life is that it is private, and if everything about all aspects of your life can be researched online that privacy vanishes. There are a lot of activities that are legal, let's say political protest, partying hard, watching porn, spending too much time playing games :), where somebody might well wish that not everybody he knows can find out all the details. As the internet has a long memory, indiscretions of your youth might well crop up many years later. And not everybody is fully aware of these potential consequences and always guarded in what he publishes on the internet.
Having anonymity on by default can save us from ourselves. And the global push towards eliminating anonymity on the internet has downsides which aren't always well balanced with the advantages of being able to catch criminals.