I'm gonna get out of the way the obvious; Sonic Adventure, Sonic Adventure 2, Shenmue, Shenmue II, Phantasy Star Online, Jet Set Radio. These are all highlight titles that really make the DC memorable, but they are also titles everyone is aware of or owns. So I'll try to include a few oddities instead that are worth a good go.
Dynamite Cop/Dynamite Deka 2
Sure it's super cheesy and not the longest game in the world. But grab a mate and this is a hilarious time. Anyone familiar with Die Hard Arcade on the Saturn (Or Arcade "Sega Titan ST-V" system) knows what to expect here. Great stuff.
WWF Royal Rumble
Again, for it's multiplayer value. Extra bonus hilarity if you play a 4 player on the Royal Rumble mode (Up to 8 wrestlers in the ring at a time) with the Widescreen 16:9 Codebreaker code turned on. It starts out fine, but the game loses track of where wrestlers are meant to be placed and they start morphing and glitching like mad! I'll leave a video link to my video showing this;
https://youtu.be/WBictFiFonk
https://youtu.be/WBictFiFonk
Re-Volt
This was an excellent and underrated game with some amazing tracks and the ability to build your own. This meant you could build some evil race courses and play 4-way multiplayers to offend your mates. Great stuff.
Metropolis Street Racer
The only downside I have to this game, and it's completely attributed to my lack of skill at it, is that it's VERY tough. I've still yet to complete the first set of races in single player. Insane. However this is the first ever title to include photo-realistic and mapped cityscapes to race around in. Race circuits had been mapped for title before, but not the cities of London, Tokyo and San Francisco (Unsurprisingly, the cities SEGA Japan, Sega America and Sega Europe all resided in). The team that made this went on to make the excellent Project Gotham Racing series - in fact MSR is the originator of many staples of modern racing games.
It introduced the Kudos system. Prior to this, the only element of racing was finishing first. Now style, control and damage all attributed to your overall victory. This would continue under the same name in the PGR series. In fact, it could be argued "PGR" was 5 games long, despite ending at PGR 4, due to this predecessor. First game with an in-built radio system for music too, albeit all pre-recorded radio DJs. Music rocks too, it's all by Richard Jacques.
Soul Calibur
The definitive version of this game is a DC exclusive. Yes it's been re-released on Xbox 360 (And likely can be played on Xbox One by now) as a downloadable title, and the graphics there will be a little cleaner. However the DC version still outputs a slick 480p at 60fps via VGA, and upscaled that's pretty darn good.
But this version is the definitive version not because of graphics (which were exceptional for the time) but because of the story mode added exclusively to it. The X360 rerelease was an arcade port so missed this crucial feature. In it, you travel across a vast map on your quest to find the Soul Edge. You play as multiple characters across multiple challenges, with special event conditions etc, earning money to unlock special features. Basically, the Dreamcast version includes everything in the X360 arcade port and adds to it. I was so disappointed that Namco didn't transfer this version, but I guess that keeps the DC version special.
Sonic Shuffle
The last remaining Sonic exclusive on the system, Shuffle was SEGA's attempt to take on the Mario Party series head-on. It certainly looked nicer, employing the cel-shaded graphics that were first realised in Jet Set Radio. It also replaced the dice-roll with a card mechanic, requiring a VMU in the front slot of the controller to see what moves you actually had available. What was interesting is you could pick one of your numbered cards, or if you didn't have the number you wanted you could steal someone else's card instead, but you'd have to choose without knowing what they had, meaning you basically took a chance at picking the right card from your opponents. This made 4-way multiplayers more treacherous and fun.
The mini-games were generally excellent too, with only a few fluffers. The ones of random chance or 3vs1/1vs3 tended to last the best once you were used to the game. In fact the mini-games were often more fun to return to than the levels themselves.
Which leads me to the few downsides Shuffle has. The boards are quite dull and not coherent with the Sonic universe, which is a big shame. The other is the loading times. To be fair, I never had an issue with the loading times, they aren't THAT long, but it seems to be a bone of contention for many so I may as well mention it.
Power Stone 2
Capcom's Power Stone is a great game in it's own right, and as a 1vs1 game it's actually a bit better than Power Stone 2. However Power Stone 2 wrecked the 4-way multiplayer in a way that even rivalled Smash Bros. Both still practically DC exclusives, I'd recommend both but Power Stone 2 is definitely my favourite of the two, with it's constantly changing playing fields adding more suspense to every match. I actually don't have a copy of this anymore, and desperately want to grab a new copy - however I hear there are differences between the regions.
The JP copy runs 60hz but has lots more glitches and issues.
The US copy runs 60hz but demands a high price.
The PAL copy may run 60hz (reports conflict) but is about the same price as the JP copy.
Choose wisely. Definitely get the US copy if you can find it cheap.
Evolution
Last one for today, but Evolution was a great RPG. Had great memories of this game, which I again don't own anymore (When I left the family home in 2010, my brother kept most of the DC games and I had to rebuild my library). This game has charm, great battle mechanics and a large explorable world with a great story. The only thing is you sometimes get annoyed with how frequently you run into random battles, but it's a small irritation overall. There is Evolution 2 on the Dreamcast, but I've not yet had a chance to play it.
Hope those are a few interesting choices for some people anyway

A few games I played and loved demos of but haven't owned the full game;
Super Runabout
Street Fighter Alpha 3/Street Fighter Zero 3 (In Japan)
Slave Zero
Rayman 2
Speed Devils Online (Especially when it's back online!)
Tokyo Highway Challenge 2/Tokyo Xtreme Racer 2