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)
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.