Ask HN: Is it possible to stay completely anonymous on the internet?

With all the security concerns recently, I've been itching to ask the question, is it even possible for an individual to stay completely anonymous every time they log on to the internet?

If not, what's their best bet or the maximum way they can protect themselves.

Ugh. Whilst I respect Stallman and what he's done, I think he's abit out of touch with reality.

Essentially is there a way to still stay off the radar, or safe, without having to completely disband yourself from society.