I would like to take this moment to say that people often misuse the terms "hacker", "hacking", and other similar words related to computer security on the internet. Saying that hackers or hacking are bad is like saying all black people do is jack cars and rap wit' their gangsta homeboys all day. I myself am a hacker, but you won't find me snooping about in your personal files. Don't have a clue how to do that, and don't intend to.
You don't need to be afraid of being labeled as a "hacker" here, it's not like the red scare where you were screwed if you were labeled a communist. It is an unfortunate thing that hackers have been given a bad name on the internet, as a lot of virus/hacker-destroyed-my-computer stories are often the fault of the user himself, for lack of proper computer maintenance. But anyway, back to the point.
Routers generally do have hardware firewalls built in. My own DSL router, a 2Wire Homeportal, has a rather robust firewall installed within its electronic innards. Though it's always good to have a software firewall to fall back on, for which I too suggest Zonealarm. It's better and more easily configurable than most other software firewalls out there, and the standard version is free for home use.
In conclusion, you can rest assured that no one is going to be hacking your computer while you're netgaming unless they found some way to execute malicious code from within a wad file, which I imagine the kind programmers have done their best to prevent happening. Of course there is always that remote possibility, no program is flawless in security, but the odds are stacked massively against it in this case.
Man, that was a really long post.