My brother bought a Dreamcast years ago off of eBay (making it one of the few non-Nintendo consoles in the house) along with a bunch of games. Probably in impulse thing: other than Marvel Vs. Capcom 2, I don't think he finished the other games that came with it. (However I think that game is on PS2 and downloadable for PS3, both of which should be easier to find.)
He wanted it mostly to play Shenmue, which seems like a deep adventure game, but he couldn't ever beat the forklift races.
There's also Skies Of Arcadia if you like RPGs or Ikaruga if you like really difficult vertical space shooters (I could never beat the second boss, one of the most shameful of my few "games I never finished"), but both are also on the GameCube.
I can't really think of many truly-exclusive must-play games for the Dreamcast, most have since been ported to the PS2/GameCube/Xbox, I believe.