I think the best way to see what games are WiFi enabled is to go to Nintendo's site. Somewhere in the DS section, you can click on the WiFi logo and it lets you choose to list all WiFi enabled games. I only just got my DS myself and like some other people have said, I actually haven't really played my Wii since I got DS. I got to the last chapter in Super Paper Mario about 3 weeks ago and haven't touched it since.
As far as what people have said about friend codes, you don't *NEED* friend codes for most games. You can play random worldwide opponents, but it's a bit limited to how you can communicate with them or other various options.
Another good place to check out for a lot of info is Wikipedia (of course) and just look up Nintendo WFC.