Marvel vs. Capcom (the original) had a speed option that allowed for fights that lasted only a few seconds. The first night I got it and found this feature, my roommate and I (we had just moved into our first apartment after college) called all of our friends over and had a series of fast tournaments. The most amazing part was that the controls were so accurate despite being played so incredibly fast. Something like 15 friends ended up coming and we played for hours trading off characters and players. It was a ball. I've never seen such a feature on any other game before or since.
Grandia II might be the best JRPG of all time (on the Dramcast that is). Incredible story, characters, graphics and battle system. Basically the perfect JRPG.
Soul Calibur II was definitely the best fighter for ANY console EVER. The graphics were amazing and still are, the controls were smooth as silk and the extra options/challenges/features/modes....well lets just say there were LOTS of them.
Also, the internet and keyboard worked well with the console at the time.
Before the Dreamcast I wasn't a fan of Sega. The Dreamcast was possibly the best console ever made (as far as being one that was made for gamers of its day that is). It was really sad when we found out that it was being discontinued. It was a few years before I bought a used Playstation 2, a really good system with tons of good games, but the unique feeling of the Dreamcast and its games never returned. They were just FUN. Not kiddie fun (Wii), not Playstation fun, just a joy to play.