I'm not a big gamer on my DS, mostly because I'm going to wait for the 3DS to hit the scene before I start investing in Nintendo again. But the games I have played for the DS that I enjoyed were: Animal Crossing: Wild World Pokemon Heart Gold/Soul Silver Super Mario 64 DS New Super Mario Bros. If you're a Kingdom Hearts fan: watch out! Apparently the DS versions of anything Kingdom Hearts related is full of suck.
I haven't played my DS nearly as much as the ol' fashioned gameboy pocket but I can definitely can recommend Pokemon Soul Silver or Heart Gold if you are a fan of the pokemon games.
I've owned a ds lite for a few years and have loved it. Games played are: -new super Mario bros -cod mod. Warfare mobilized -pokemon platinum/soulsilver -super Mario 64 ds -guitar hero ds DS is a cool system but they are too expensive for the new ones. 160-170 for a handheld? No thank you.