Dont think that just because you are behind a router you are safe and dont need a firewall as some have said. Routers can be by-passed in numerous ways. If someone does by-pass your router and you have no other protection whats to stop an attacker from doing what he wants??

Also, yes a router will stop the casual attacker but what stops programs on your computer from accessing other networks/internet etc?? You need a software firewall on your box, even if it is just for program control.