It would be entirely possible to design a WiFi-enabled peripheral that attaches to a joystick port that would allow you to play against someone over the Internet. Depending on the quality of your Internet connection, a turn-based game like chess would probably be better than, say, Warlords. It'd be a lot of work, but it's definitely possible.
Similarly, you could design a WiFi-enabled cartridge. Heck, you could even design a "Twitter" cartridge that would display your Twitter feed as text that you could then shoot for points with a spaceship controlled by your joystick. The possibilities are endless.
--Will