Wow. uhm.  You can go tons of directions with Dreamcast, but I personally hate sports games/3d platformers.  That said, here's my collection:
US
Sega Smash Pack Vol 1 - why isn't Golden Axe a two-player?  Virtua Cop 2 is more fun than I remembered, tho.  
Sonic Adventure (blah)
Sonic Adventure 2  - Okay, but a little boring 
Crazi Taxi - Alright every once in awhile
Marvel vs Capcom - Good game, better music than sequel.
Marvel vs Capcom 2 - Best port, since NAOMI is a Dreamcast.
Plasma Blade - Dated graphics for a 3d fighter, pretty fun though.
Dead or Alive 2 - Fun for the four-player tags, that's it.
Soul Calibur - Good stuff from Namco.
House of the Dead 2 - Fun, but gets old quick.
Confidential Mission - Another light-gun game.  So-so.
Bangai-O - Hilarious and weird, crazy fun.
Street Fighter 3 Third Strike - Awesome fighter.
Mars Matrix - Crazy technical/manic shooter by Capcom.
Giga Wing - Flashy shooter, good stuff by Capcom.
Cannon Spike - Weird smash tv-ish shooter.  Capcom.
Fatal Fury Mark of the Wolves - Great 2d Fighter.  Not so much as Street Fighter 3 3rd strike, but better than 2nd Impact.
Last Blade 2 - Samurai Shodown style game.  Incredibly censored, but fun in its own way.  I prefer the SS games, really, but there are lots of people who go the other way.  
I've got another Capcom/Psikyo, can't remember its name, but shooter fans know it probably.  It's a cute'em up with the witch, robot, Alucard, Morrigan, the guy on a rug, etc.  Psikyo almost always plays the same - boring for me, but to someone new they're awesome.
Capcom vs SNK - Awesome, better music and graphics than sequel but more "broken".  
JAP
Ikaruga - prime shooter for the system, only JAP, but available in US on Gamecube.
Border Down - weird, sorta like Gradius/R Type with Metal Black
What's that Psikyo helicopter game with the 360 turning radius?  Eh, this is shooter just like all over the other Psikyos with a turning function.  Interesting for a second, but lame music and stuff puts it down.
I would recommend most of those, but I won't sell shooters just for "completeness" sake.  Otherwise I would ditch anything partially made by Psikyo.  The fighters are basically all top-notch for one reason or another, and Bangai-O is nutsy fun.  
Hope that helps.