I wish I had more than one vote because a lot of the comments written about other consoles (other than the Megadrive which got my vote) brings back sooo many memories.
I nearly ruined my GCSEs because of Goldeneye on the N64 (oh how unimportant they seem now!) We used to play the N64 four player for hours on end and we used to play drinking games, whoever lost at Mario Kart, Goldeneye, Snowboard Kids (From what I can remember) had to do a shot of the flithiest shot we could find in the cupboard (not including cleaning chemicals) And playing Zelda: OOT and Mario 64 where major highlights in my gaming past, they had so much charisma, level design second to none and best of all, playability by the bucket load. I think Mario 64 is the only 1 player game I've ever played with 4 people (taking it in turns).
As for the Dreamcast, well simply wow. This system has lasted me years, and I've been playing it quite a bit recently (my mates DC actually, I broke mine). Virtua Tennis (2 really) is one of the best sports games of all time, and playing it four player is a superb idea (even if you hate tennis), talk about learning curve. And who can forgot the classics such as Skies of Arcadia, Grandia 2, Shenmue 1+2, MSR, the sublime Rez and (only recently bettered) Soul Calibur. Then you have the quick fix Crazy Taxi's, the undeniably 'old-school' MDK2 (one of the most difficult games I have played in recent years), and Quake 3 Arena and Unreal Tournament (Both great conversions). But for drunken mayhem it really does have to be Chu Chu Rocket, my god that game makes your head hurt. And not forgetting to mention Bomberman Online, and Worms World Party. Those games kick serious ass too. Oh my god I forgot about the Arcade perfect conversions of the old-school games! (2D fighter, shmups). Gigawing (1+2), Gunbird 2, Ikaruga, Street Fighter Alhpa 3, Street Fighter 3 (All versions), Capcom Vs SNK (1+2), the list goes OOOOON.
The Saturn was also a big fave of mine. I was a BIG fan of Virtua Cop 1 and 2 and played them for hours over and over trying to get my score multiplier up as far as possible (involving never being shot and not killing hostages). Virtua Fighter 2 was groundbreaking for the time, having superb hi-res graphics and a combat system that still retains it charms and has only really been 'polished' since. I have much to say about Nights as it blew me away. It was so much more about linking and chaining rather than completing the levels and getting A's on all every level was a great achievement for me, but didn't stop me going back and playing it AGAIN and AGAIN. Unfortunately I never played Shining Force 3, but I did play (and still own) the AWESOME Panzer Dragoon Saga, 4 disks of sheer brilliance, both 'prequels' (if you can call em that?) being defining points in the Saturn's life. Ugh the list is endless! Guardian Heroes, Radiant Silvergun (nice ones Treasure!), Burning Rangers, Tomb Raider (yes this game was awesome and ground breaking - pity about the mess they made of the series), Children of the Atom, Marvel Vs Streetfighter and the AWESOME Saturn Bomberman (10 players of fucking mayhem).
I'll leave my rants there as I could go on FOREVER. I never thought I'd have that many memories of those systems, and I've probably forgotten loads of games anyway!