First, welcome to BC!
Let me try to answer your question this way: About six months ago, my computer was really messed-up with malware. I'd been running with AVG, but no firewall. BC put my machine back on the road and I installed a firewall (Zone Alarm). Since that time, no problems, however ZA reports there have been almost 6200 intrustion attempts (that's about 35 per day), almost 100 of which were considered "high-rated". BTW, those numbers based on about 2 hours per day surfing relatively safe news sites and similar; nothing out of the ordinary.
So I think a firewall is extremely
important, along with regularly updated AV and malware-detecting software. A great BC Tutorial on protecting your computer can be found here
and a BC Tutorial on firewalls can be found here.