Virtual On: Oratorio Tangram, although it's best experienced with the Dreamcast Twin Stick. I recently got a Dragoncast VS. Link Cable for the game. Niice.
Ecco the Dolphin: Defender of the Future - You must think like a dolphin in order to finish this game, the puzzles are tough but very rewarding. Resident Evil: Code Veronica - My favourite resi game. The incest between the two lead villians just makes the whole thing much more creepy. And surprise cameo by + - Wesker . The Lost Golem - a lovely little puzzle game. Simple but charming. Sega Tetris - makes up for a lack of monkey ball on DC. Mallet swinging monkeys improve tetris experience. Cosmic Smash - Virtua Tennis meets Rez meets Breakout in spectacular fashion. Tokyo Bus Driver - The antithesis of Crazy Taxi, but somehow just as fun.
Oshi, I forgot that. I don't even care that much for the original series and I thought Ecco 3D was goddamn fantastic. If you can find it, the PS2 version is also excellent (and probably much better controls).
Shame on every last one of you for not mentioning this. Gather some friends for this one. My nephews and I played the hell out of it back in the day. Also, all the ports suck. This is the one you want.
I've got Rush 2049, and I think I'd like it a lot more if the cars weren't totalled by the average butterfly. =( Also, Eggfan reminds me of how badly I need Cosmic Smash. New year present to myself, I think.
I was gonna say SA2, but I thought that mabye a bit too obvious, given our current location, you got a DC, you want games, your asking on Sonicretro, you probably already got SA1/2 ordered and in the mail XD
Tech Romancer is pretty awesome. It's a fighting game by Capcom about fighting mecha. Sort of like Cyberbots: Full Metal Madness, if you've ever played that, and Jin's a secret character. The controls are a tad more complicated than your average fighting game, however.
Alrighty I'll list even though most have been mentioned before. Jet Set Radio Sonic Adventure (2 isn't bad either) Mr.Driller Shenmue Bangai-o Super Magnetic Neo Skies of Arcadia
Seconding Doc Eggfan's recommendation of Cosmic Smash heavily, as well as Aquaslash's recommendation of Rush 2049. If you're a wrestling game fan, you can't go wrong with Fire Pro Wrestling D. Street Fighter 3: Third Strike, Garou: Mark of the Wolves, Capcom vs. SNK 2 for 2D fighting game fans. There's many more, but I can't think of anything else I want to add.
As if you didn't know my answer already. Shenmue (hurrr) Shenmue II Crazy Taxi Skies of Arcadia Jet Set Radio Grandia II Cosmic Smash (fantastic game) Dead or Alive 2 NBA 2k2 (seriously, the only basketball game I like, and it's good) If you can get the microphone, Seaman Legacy of Kain: Soul Reaver God, I miss the Dreamcast.
Tech Romancer's controls are actually pretty simple among fighting games, I actually think it's a great sort of introductory game to the genre. It's also one of the funny games that's actually better on the Dreamcast than in the arcade. Interestingly, reading through this thread is giving me a better impression of why arcades seem to be on the way out and why the Dreamcast fizzled.
I take it you guys saw the Top 100 Dreamcast games poll I did a few months ago? If not: http://dreamcast100.blogspot.com/ Based on how many voters joined in it's the most definitive fan list on the net as far as I know, yet there's still a lot of great games that didn't make the Top 100 (and some I was quite surprised did make it in, like the Resident Evil 2 and 3 ports).
Here are some lesser known games I enjoyed: Soul Fighter Death Crimson OX Dynamite Cop! Tokyo Xtreme Racer 2 Omikron: The Nomad Soul - This one is rumored to be getting a PS3 exlusive sequel
Jet Set Radio. I only bought cause it was £9.99 back in December, but wow. It's just one of the best games I've ever played. There's some pretty obvious flaws, and the controls can feel so unrealistically clunky at times but the overall experience is simply fantastic. I've got to get off my ass and buy the Xbox and GBA games now.
The GBA game isn't really worth getting, it's a bit of a mess. I haven't played future but I've always wanted to because the first is one of my favourite games.
I can't believe no one meantioned Fur Fighters! It's like Spyro with guns! One of the best games I've ever played, it's easily the Ocarina of Time of the Dreamcast. Slave Zero is also fun, it's got very creepy atmosphere and you get to blow a lot of shit up.