Can't say I care for gaming past the 2D cartridge era, but I'd be lying if I said the Dreamcast wasn't the most fun I've had since, so I'll suggest these:
North American releases(not mentioned yet):
Grandia II - most fun you'll have with a turn based menu system, still the best release so far.
Time Stalkers - Climax(LandStalker, Lady Stalker, & Shining in the Darkness, in particular) crossover rogue-like dungeon explorer, that's usually misunderstood for not having been a well told story during the era when FMV's were overtaking the genre. There's tons to do after the very short main story(including following the smaller NPC stories).
Evolution - the sequel might be better gotten through the Gamecube version, but the entirety of the original is exclusive to this one. Same boat as Time Stalkers, it's more of a treasure hunting dungeon crawler than a story.
Dynamite Cop - it's amazing they never got around to a 4th Streets of Rage, because Sega pulled off 3D beat 'em ups at this point in time, when everyone else kind of sucked at them.
E.G.G.: Elemental Gimmick Gear - the obligatory action/adventure game, with hand drawn art, and 3D boss battles.
Power Stone II - Some prefer the original, this one gets crazier, with more interactive stages and the like
Cannon Spike - rollerskate run 'n gun Capcom crossover(if I remember correctly Cammy, Mega Man and Arthur(G'nG) are in this, possibly B. B. Hood(Darkstalkers) as well)
The House of the Dead 2 - awesome light gun game, with B-movie acting, but you'd need a CRT if you picked it up for the actual console.
Heavy Metal GeoMatrix/Spawn: in the Demon's Hand - similar arena fighters as the Power Stone games, but with their own twists, and the licenses attached to them. Also by Capcom(when they were at their best)
Japanese exclusives:
Wrestling fans can't go wrong with any of the options here.
Godzilla Generations Maximum Impact - rail shooter with the Panzer Dragoon/E-102(Sonic Adventure) style targeting.