These aren't all games that necessarily sold me on the system, but they're games that could have, and some of the first/best games I owned/played for each system. -
================NINTENDO CONSOLES================
NES - Super Mario, Duck Hunt
SNES - Super Mario World, Super Mario All-Stars, Donkey Kong Country, MegaMan X, Super Castlevania IV
N64 - Super Mario 64, Super Smash Bros, Diddy Kong Racing, Donkey Kong 64
Gamecube - Super Mario Sunshine, Super Smash Bros Melee, Mario Kart Double Dash
Wii - Super Mario Galaxy, Super Mario Galaxy 2, Super Paper Mario, Super Smash Bros Brawl, Donkey Kong Country Returns, Mario Kart Wii, Kirby's Epic Yarn
Wii U - Super Mario 3D World, Donkey Kong Country Tropical Freeze, Monster Hunter 3 Ultimate, Legend Of Zelda:Wind Waker HD, new Legend Of Zelda, Yarn Yoshi
================NINTENDO HANDHELDS================
Game Boy - Tetris
Game Boy Color - Pokemon Blue, Pokemon Gold, Azure Dreams, Legend Of Zelda:Link's Awakening DX
Game Boy Advance - Pokemon Sapphire, Harvest Moon:Friends Of Mineral Town
DS - N/A - Tempted by lots and lots of stuff. Just never got around to it.
3DS XL - Pokemon Y, MegaMan Zero Collection
================PLAYSTATIONS================
PlayStation - MegaMan 8, MegaMan X4, Xenogears, Suikoden 2, Thousand Arms, Lunar Silver Star Story Complete, Final Fantasy Tactics, Castlevania:Symphony Of The Night, MegaMan Legends, MegaMan Legends 2, The Misadventures Of Tron Bonne, Azure Dreams
(these actually belong under PS2 since I've never owned a PS1. I played them all else where and they just made me want a PlayStation, and thus the backwards compatible PS2)
PlayStation 2 - Armored Core 2, Okami, Shadow Of The Colossus, God Of War
PlayStation 3 - Metal Gear Solid 4, Uncharted 2, Fallout 3, Assassin's Creed 2
PlayStation 4 - [PENDING] Uncharted 4, WATCH_DOGS, Resogun, Metal Gear Solid 5, Mighty No.9, Strider, Deep Down, The Division
PlayStation Portable - Final Fantasy Tactics:War Of The Lions, God Of War:Chains Of Olympus, MegaMan Maverick Hunter X, MegaMan Powered Up, Castlevania Dracula X Chronicles
PlayStation Vita - [PENDING] Remote Play with the PS4 alone will be worth it....if it works.
================XBOXES================
Xbox - I only have one because a guy was selling it for $15. Never found any games worth playing on it.
Xbox 360 - N/A - I have zero interest in owning something less reliable than my 23 year old SNES, especially when it has no worthwhile games
Xbox One - N/A - I have LESS than zero interest in owning one. The only "Xbone" game that interests me is Titanfall, and that's coming to PC...where it will be better anyways.
================SEGA SYSTEMS================
Sega Genesis - Sonic, Sonic 2
Sega Saturn - N/A Never owned or even played one, but I always kinda wanted to play NiGHTS.
Sega Dreamcast - Sonic Adventure, Power Stone
Sega Game Gear - Sonic
================COMPUTERS================
PC gaming before I owned a PC - Dinopark Tycoon, The Incredible Machine, Ski Free (damn yeti...), Odell Down Under
PC - Age Of Empires:Rise Of Rome, Age Of Empires 2:The Conquerors, Roller Coaster Tycoon, Arcanum:Of Steamworks & Magick Obscura, Diablo 2:Lord Of Destruction, SimCity 2000.
PC Steam (totally counts as its own platform) - Portal, Team Fortress 2, Left 4 Dead. (One of those games is what installed Steam initially. I think it was Left 4 Dead. Now here I am, like 250 games later, with it as my primary platform)
================OTHER================
iPad 2 - Final Fantasy Tactics:War Of The Lions, Kingdom Rush, Plague Inc, Minecraft, MegaMan 2
(I was actually randomly given the iPad for Christmas. *shrug*)