I'm not much of a fighting or Sports games guy, but there are a few of those I enjoy on Dreamcast, so I'm listing some of my favorites regardless of instruction

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*Bangai-O - zany 2d shooter with great use of Engrish dialog and the ability to fire hundreds of missiles at your targets? what more could you ask for.
*Chu Chu Rocket - great puzzle game
*Crazy Taxi - Still great fun after all these years, pick up passengers and go, though its best as a title to plunk in for 30 or 40 minutes at a time when you get tired of playing the main game your on.
*Deep Fighter - yes, it has cheesy live action FMV sequences, but the variety of tasks you get to complete on different submarines makes it a worthy purchase IMHO.
*Headhunter (Euro) - Had a lot of fun with this action inport, but if you have a PS2 its probably just as easy to buy the version released in the states.
*Hydro Thunder - Not quite as fun as sitting in the chair with throttle in hand at the arcade, but you don't have to Pay per play either

*Legacy of Kain: Soul Reaver - Much better than the PS1 version, good dark platformer.
*Mars Matrix - This is quite a challenging top-down shooter, will make you pull your hair out, but before long you'll be back at it.
*MDK2 - 3 game styles in one, balls to the wall 4 fisited blasting, stealthy sniping, and a puzzlers, all encompased with a quirky sense of humor, though it can be a bit challenging.
*Power Stone 1 + 2 - Ya, i know you say you don't really like want fighting games, 1 is the more serious fighter, but 2 is more similar to Super Smash Brothers so if have 3 other peeps who don't mind playing "outdated" technology, you'll have a blast.
*Record of Lodoss War- Pretty good action RPG, but youll enjoy it much more if your a fan of the anime.
*Rez (euro or JPN) - On the rails shooter that has to be experienced, can't really describe it, and remember "Fear is the mind killer". If there was a VG up to this point which could be called interactive art, it would be this game.
*San Francisco Rush 2049 - My absolute favorite of the Rush games, crisp graphics, crazy tracks, and the retractable wings were a great addition, I have blown hours just messing around in the stunt courses alone.
*Shadow Man - Great story, great voice acting, great architecture, creepy as hell, I still remember freaking out the first time I heard and saw the hook monsters when playing the PC demo. Later stages become progressively creepier, just be careful if you have to read FAQs when figuring it out, or you might hit a spoiler for the end of the game.
*Sword of the Berserk - good, bloody fun for a 3d hack and slash, Got me interested enough that i checked out the anime it was based on (that was good too, though it deals with many mature themes) I was really bummed when they decided not to release the Berserk PS2 game in the states as it takes off right when the series ends.
*Typing of the Dead - House of the Dead 2 reworked as a typing teacher, if they ever wanted to teach teenagers how to type, this would be the game to do it, even sports multiplayer if you can track down a second keyboard. Bloody good fun AND educational, suck it Jack Thompson.
*Vigilante 8: 2nd Offense - Personally, i liked the original car combat game better, but this is an adequate follow up which adds some new game mechanics. Loads of fun if you can get a multiplayer game started.
*Virtual On: Oratorio Tangram - Bad sub-line, great mech combat game. There are two schools of thought, slow tank-like mechs, and graceful, nimble anime-style mechs, this game is the ladder. Though Zone of the Enders: 2nd Runner pretty much blows this game away in terms of single player, multiplayer is still pretty enjoyable.
Anyway you slice it, there are more good games for the DC than you'll ever be able to find the time to play, trust me

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Edit: Oh, and another vote for Sega Marine Fishing, its easier with a normal controller, but much more authentic with the fishing controller.