When I first got broadband, I was using a Linksys router (along with the Cisco 675 the DSL provider sent me) and figured the network address translation would be like a firewall... more or less.
One day I was shutting down my PC and a dialog box popped up. Something like:
If you shut down, user GIORDI will be disconnected. Continue?
!!?!??!?
Next time I booted up, first thing I did was install ZoneAlarm. It logs plenty of suspicious traffic attempting to reach my computer, although I'm under the impression that most of it is innocuous. I haven't a clue how this gets past the router, but maybe I have something misconfigured (but no, I don't have a DMZ set up...). FWIW, I'm running Windows XP and haven't had any trouble with ZoneAlarm. I'm running the free version of 2.6.