Well, I said this in December, and I'm happy to announce that I finally have a Sega Dreamcast. Unfortunately, my first game (Sonic Adventure) doesn't arrive for another two weeks. 
The Sega Dreamcast is hands down my favorite system, and it is also a great system to own cause "ripping" games is child's play. (I never did this during it's original lifecycle though.)
What kinda games do you like?
I'll run down some of my favorites... Most of my favs are "arcade" games. Loud and colorful. I enjoy the style.
FightingRival Schools Project Justice: A beautiful, quirky 3D Capcom fighter. I love the cast.
Cyber Troopers Virtual-On Oratorio Tangram: Robots, impossible to beat final boss without the original arcade stick sadly
RPG/AdventureShenmue I and II: I hesitant to suggest it cause if you really start to enjoy it you will just kinda be left hanging... you can only get II with the PAL version.
Skies of Arcadia: I'd say if it the best JRPG on the console.
Evolution 1 and 2: If you like dungeons
ArcadeZombie Revenge: Not a great game by any means, but it is a goofy arcade game with horrible voice acting. I love it.
18 Wheeler American Pro Trucker: I dunno, it's fun.
RacingSega GT: At the time it was better than Gran Turismo 1 or 2, imo. Modern games blow it out the water though.
Sega Rally 2: Still fun
OtherJet Grind Radio: The controls have aged a lil, and you can find it on other platforms but wow it is great. Get the NA version. More content.
Gundam Side Story 0079: Robot dueling