To me, it depends on what we're talking about.
Private phone calls or e-mails between private individuals? The government can get a warrant, or it can piss right off. A warrant requires they show reasonable cause to suspect I've done something wrong, first.
However, when it comes to greater Internet behaviour, like participation in online forums and the like, you've breached privacy, by posting in public. Same goes for Facebook and Twitter and whatnot. That the government can connect your online public activity with your real self is not, IMO, something covered by privacy laws. The only cases where it becomes an issue are authoritarian countries, like Iran, where these services are often the only means for the public to organize dissent, relying on that anonymity. But really, if I think this ceased to be protected, nobody would make the mistake of doing so online, any more. And there would be means to have private-access sites that effectively let similar-minded people discuss things in private, and since they aren't public-access, this principle wouldn't apply (I'm only applying it to public-access services like Twitter and web forums like this one).