Personally, when it comes to computer security, I try to err on the side of paranoia. So that means taht not only do I have a router but I am also running a software firewall (zonealarm). I like zonealarm because if I get infected by any viruses, once my rules are setup, it will tell me if the program has changed since it last accessed the internet, and also tell me if something new (that I might not be aware is running) is trying to access the internet.
Besides, the software firewall may provide you with some extra time to patch/clean your system when new viruses/exploits come out.
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