Absolutely, and if you were using BitCoin for primarily things that could get a search warrant issued, you'd take steps to protect your anonymity. However, BTC is not some currency designed for those kinds of activities any more than Google was designed to promote file sharing by indexing .torrent files. When buying online I generally use my real name (so I can sign for it or have it delivered to work), I HAVE to use my real address (or work address), and the Tor network is too slow to bother with regular purchases.

If at any point in the past or future I wanted to buy the eBook "Is My Wife Cheating On Me" and was worried my political opponents would use it against me, the address I used above could be used to link my BitCoin address to me. And because you have to spend money with the same address with which it was received, it's all too easy to accidently spend money that's tied to your ID.

In other words, have two wallets! One that is ONLY used for anonymous activity.