Sea Man. Strangest video game I've ever had, Only one I've ever had that I could talk to.. and also the only one that has ever nagged at me before about skipping school.
Jet Grind Radio
Shenmue
Power Stone 1/2
Soul Caliber
Sonic adventure 1/2 for the times that you play sonic.
Sega GT(online), not all that realistic but I really dug the car selection and music soundtrack!!!
Skies of Arcadia and Grandia2 if you like RPG's.
Marvel vs Capcom 2
Rayman 2
Resident Evil Code: Veronica
Virtual On: Oratorio Tangram
Soul Reaver:Legacy of Kain
Sword of the Berserk
Gundam Rise from the Ashes
Phantasy Star Online was also really good but I don't think it is playable online anymore.

And Quake III arena on the dreamcast has sucked more of my time away then just about every other video game I have played by a long shot. Probably played more q3 then I have any other game combined. Great stuff. But I'd just play it on the PC instead, in fact QuakeLive is in works and it will be free q3+tweaks that launches from your browser. Having beta tested it I can say it is fantastic.
There are more DC games that I liked but I dont remember at this time. but after listing some of those I'm tempted to get another dreamcast! I dont think there has been a console since then that has come close to matching it as far as variety of unique and high quality games! And the fact that I was able to play and surf online on that thing for free years before microsoft opened up it's charged service easily makes it my favorite console to date.