I would think not =)
Havn't used anti-virus programs for years now, the web-based ones are just as good as any of the versions you find in the store.
As for firewalls, assuming you are using Win XP, then the built-in firewall shouldn't be any worse than ZoneAlarm, so why use more than you have to?
As I have no interest in knowing who's trying to get in to my computer, but only preventing it from happening in the first place, I'm happy to stick with XPs default firewall. Should one want more specific info of intrusion attempts then maybe a stand-alone programme like ZoneAlarm may be good.
Fly safely!
/Magnus