I think the Dreamcast is probably my favorite system ever, just barely nudging out the N64/SNES/NES. I think more things in modern consoles can be traced to it than possibly any other.
Its strange, I hate so many things about the Wii's addons, but I liked them with the Dreamcast. The VMUs were completely impractical (awful battery life with relatively difficult to locate batteries), but they were charming.
It wasn't a big multi-player system for me oddly enough, I think House of the Dead 2 was the only one. I loved that game, even though it was short was pretty repetitive, and the crappy off-brand lightguns we got stuck with because Sega wouldn't localise their own, sucked, but it was still a blast with two players (I think we had fun even when playing with the regular controllers). I played the crap out of TXR2 in the dearth of time between Gran Turismos.
I liked Sonic although there was plenty about it that wasn't that good (the big stupid cat with the fishing thing). Record of Lodoss War was a decent dungeon crawler, although no co-op sucked. At the time, I hated fighting games for some reason, and never got into Soul Calibur although I could see why it was highly rated. I'm trying to remember other games that I played. I really did not play all that many and missed plenty of the really good ones. Oh yeah, I remember really wanting to play Shadowman for some reason, and went on a big trip to track down a copy on a Sunday. I barely made it anywhere in that game and got stuck with no idea where I was supposed to go next. Oh, I remember the 2nd Vigilante 8, that was probably the only other game I really played multiplayer on it.
Looking at list of games now. Crazy Taxi! Played that a ton, swapping turns so I guess it was sorta multiplayer. Shenmue was both really silly/stupid and amazing at the same time. It had such potential, too bad they spent so much time putting a billion pointless vending machine/store things. And I forgot Code Veronica. I got stuck at the end of the first disc and I think had to cheat my way past. The knife was pretty overpowered, well somewhat, but the guns were just way to ineffective, and it took the RE story places that, well I don't really know where they're going with the RE overall storyline as they just keep adding fucked up stuff with each game past 2.
Played Shenmue II (barely), Phantasy Star Online, Skies of Arcadia, and Ikaruga later (Xbox, GC, GC). Didn't get into Dead or Alive until 3 on the Xbox, but 2 is where the franchise really seemed to take off.
Blah, ok, I don't know why I completely ignored NFL2K. It was one of the games I bought the system for (big wow factor).
Really, I don't know why I'm so fond of it, as at best, I'd say the games I played on it were maybe 8.5s. NFL2K probably a 9 since it really pushed things forward, but pretty much all of the games I played had some significant deductions. I think they hit that sweet spot between really great and mediocre, like that band you really dug in high school and still listen to fondly but you know they're not really all that good but you still love it anyways.