Power Stone 1/2
Rival Schools (Project Justice)
Marvel Vs Capcom 1/2
Vigilante 8 (twisted metal style)
Virtua Cop2 , Virtua Fighter series
Street Fighter Alpha 3 + 3rd Strike
Ikaruga
Once you beat shenmue, getting II is a must!
Berserk (based off manga), great game
Capcom Vs SNK I/II
Unreal Tournament (imo not really worth it due to controls but runs great)
Dead or Alive  series (if not already played)
MDK 2 < this was one of my fav's on the DC
House of the dead 2
Soul Caliber
Sonic Adventure 1 / 2
There was a star wars game too that was decent but I dont remember which
~
The biggest mistake I made was trading my dreamcast for a modded PSX. -_-

I love my Dreamcast, though I don't play it as much as I should.  My favorite games are Jet Grind Radio, Space Channel 5, Typing of the Dead, SF Third Strike, and above all else Roommania #203.  Roommania #203 requires a guide to play if you don't know Japanese (well you can probably make it for a while without one but I don't see you completing it), but it's incredibly cool.

I personally spent a lot of time with Jet Grind Radio, Sonic Adventure 2(for some reason I loved playing Sonic's last level and the final boss fights over and over) and Rez, which I'm surprised hasn't been brought up yet. I've also enjoyed a couple other games that have been mentioned(including all the ones in the op), but those ones are the first ones to pop into my head.

I forgot about Rez just because the XBLA version is the only one I've played.  Actually finding the Dreamcast version is a pain (although it sounds like he's downloading games anyway so yes play Rez)

I miss my dreamcast but what I had for it was:

Skies of Arcadia (da best)
Sonic Adventure
Sonic Adventure 2 (sucks)
Crazy Taxi (aww yeah)

umm and some other shit you get the point. 

edit: and I always wished I had Typing of the Dead but what are you gonna do

Crazy Taxi (aww yeah)

more like aww YAH YAH YAH YAH YAH

I got lucky and found a Dreamcast keyboard and mouse cheap on eBay.  Typing of the Dead is so good.  But if you really wanna play it there's always a PC version.

Crazy taxi is quality, but I feel like the challenge mod is SO damn difficult. I got most of the 1 and 2 level stuff, but theres a couple of the 3 that are ridiculous.

Bad religion songs all the way also Crazy taxi 2 sucks never get that one because it's a piece of shit.

Also I disagrees with roman Sonic Adventure 2 dose not suck and it better then the first to me

Tried out Space Channel 5, its harder then I thought it would be since I you have to time you movements with the beat alone and I pretty much have to have scrolling arrows/color coded buttons to do this shit. Hopefully a little practice is all I need though.

Tried out Space Channel 5, its harder then I thought it would be since I you have to time you movements with the beat alone and I pretty much have to have scrolling arrows/color coded buttons to do this shit. Hopefully a little practice is all I need though.

Yeah if you're used to other music games it takes some getting used to but you'll get the hang of it.  I don't know if it came out on Dreamcast at all but if you like it you should check out Space Channel 5 Part 2 (I think it's available as part of that Dreamcast Classics pack on 360/PS3/(PC?) and I know you can get it bundled with SC5 on the PS2 too).  Really funky and also has Michael Jackson voicing himself.

Another game that came to mind when I used to have a keyboard + online for the dreamcast; Phantasy Star. I doubt you can still play it though (online).
Soul Reaver was a badass game too. Play it if you haven't already.

I'd say that Sonic Adventure is probably only good for nostalgia's sake, but Sonic Adventure 2 can never be forgiven for the Knuckles/Rouge levels.  That's seriously just the most malicious game design ever.

Phantasy Star Online is probably the only online game of any kind other than NHL games that I actually played extensively and enjoyed.  I miss that game

Also TOY COMMANDER was really cool back in the day but that's another one that hasn't aged very well

Another game that came to mind when I used to have a keyboard + online for the dreamcast; Phantasy Star. I doubt you can still play it though (online).

iirc there are a lot of private servers out there for DC games.  The problem is that I'm pretty sure you need a broadband adapter, and those are pretty pricy.  I don't know much about it though, it's worth looking into if you wanna play it.