Stealing and modifying dreama1's very ambitious thread idea.
As the title says. No real rules, feel free to twist them or define genres however you want. I'll chuck in an 'undefinable' too to give the games I can't nail a genre to a chance.
I'll skip to fourth gen for mine because I haven't played enough 8-bit games.
Fourth gen/16B
RPG - Final Fantasy VI
Platformer - Kirby's Fun Pak
Action - Castlevania: Vampire's Kiss
Puzzle/Arcade - Dragon's Fury
Shmup/Rail Shooter - Starwing
Survival Horror - Clock Tower (not exactly much competition but it's good anyway)
Fifth gen/32B/64B
RPG - Final Fantasy VIII
Platformer - Oddworld: Abe's Exoddus
Action - Monkey Hero
Puzzle/Arcade - Bust-a-Move 2
FPS - Alien Trilogy
Shmup/Rail Shooter - Panzer Dragoon
Survival Horror - Silent Hill
Fighting - Mortal Kombat 3
Sports - Tony Hawk's Pro Skater 2
Undefinable - Yu-Gi-Oh! Forbidden Memories
Sixth gen
JRPG - Shin Megami Tensei: Persona 3 FES
Pseudo-JRPG - Dark Cloud
WRPG - The Elder Scrolls III: Morrowind
Platformer - Dr. Muto
Action-Adventure - Jet Set Radio Future
Action Sandbox - Bully
Puzzle/Arcade - Puyo Pop Fever
FPS - Unreal Championship 2: The Liandri Conflict
Shmup/Rail Shooter - Panzer Dragoon Orta
Survival Horror - Silent Hill 2/Silent Hill 4: The Room (SH2's a better game, SH4's scarier, dunno which I prefer)
Fighting - Soul Calibur II
Rhythm - Guitar Hero III
Undefinable - Shenmue II
Seventh gen
JRPG - Lost Odyssey
Pseudo-JRPG - Nier
WRPG - The Elder Scrolls V: Skyrim
Platformer - Alice: Madness Returns
Adventure - 999: 9 Hours, 9 Persons, 9 Doors
Action-Adventure - Metal Gear Solid 4: Guns of the Patriots
Action Sandbox - Saints Row 2
Action Hack & Slash - No More Heroes 2: Desperate Struggle
Roguelike - Pokemon Mystery Dungeon: Blue/Red Rescue Team
Puzzle/Arcade - Katamari Forever
FPS - BioShock
Shmup/Rail Shooter - Child of Eden
Survival Horror - Amnesia: The Dark Descent
Fighting - BlazBlue: Continuum Shift
Rhythm - Beat the Beat: Rhythm Paradise
Undefinable - Yu-Gi-Oh! 5D'S World Championship 2010: Reverse of Arcadia
Eighth gen
JRPG - Persona 5
Pseudo-JRPG - Nier: Automata
WRPG - Fallout 4
Platformer - Super Mario Odyssey
Adventure - Virtue's Last Reward
Visual Novel - The House in Fata Morgana
Action-Adventure - Gravity Rush
Action Sandbox - Grand Theft Auto V
Action Hack & Slash - Bayonetta 2
Puzzle/Arcade - Lumines: Electronic Symphony
3PS - Splatoon 2
Survival Horror - Alien: Isolation
Rhythm - Superbeat XONiC
Undefinable - Freedom Wars (I guess it'd be pseudo-JRPG but I don't have anything else to put here and want to rep this game)
Pseudo-JRPG is a game everyone else calls a JRPG that I don't consider to be a JRPG and wanted an excuse to put into my list.
Show me yours!