I would not recommend running both the windows firewall and a separate firewall together, although I know some folks who do.
Very good point TeaSea, I meant to mention that, running 2 software Firewalls can cause all kinds of problems, you really have to work on the configurations of both and that is a PITA. You can do fine with a Router Firewall and an additional software firewall if you are seriously worried, but for most users that is not really necessary.