Many people take the "get pissed off" route, I've noticed. Others wait patiently(because chess takes patience). It's up to you.
Timewasters
Thanks for your comments guys. I decided the best thing to do is just start a simultaneous game (wasn't aware you could do that) rather than resign. Then block the timewaster after the clock runs out.
I think blocking unsportsmanlike players is a good idea, although a fair number of members insist on venting their spleen in the forums. I suggest you just block them and move on, my guess is the majority if not very large majority of players here are more sportsmanlike than unsportsmanlike, but that's just my unverified opinion.

Just joined the Chess this week, it's great. But can anyone advise on what to do if an opponent knows they're finished, but decides to just run the clock down or wait for me to resign? Much Appreciated.