The question is: is there a reason to NOT surf anonymously? It is not "do I have something to hide" but "do I want EVERYONE to see it"?
However, anonymity is but one part of security. Using TOR you can cover your tracks a little better. But you also want to make sure to use https when submitting sensitive information; and always ask: "do they really really need this information"?
It were nice if we had secure communications (no sniffing agents in the middle) and plausible deniability (no officer, it wasn't me).
What we do have is a little more secure ways of communication (by encryption) but no plausible deniability.
However all this does not help, when the site we use is operated by less nice people. And we do not have a usable way of checking their credibility, their "reputation": certificates can be and are forged, DNS is poisoned.
All I can say is: be careful whom you are dealing with.
In German "Trau, schau wem"