NES: Legend of Zelda, Super Mario 3, Crash and the Boys: Street Challenge

SNES: Secret of Mana, Super Mario World, Chrono Trigger

Genesis: Altered Beast, Shining Force, Shining Force 2

Sega CD: Vay, Popful Mail, Lunar Silver Star Story

Sega Saturn: Dragon Force

Playstation: Mortal Kombat Trilogy, Final Fantasy Tactics, Vagrant Story

N64: Wreslemania 2000, Mario 64, Killer Instinct Gold

Dreamcast: NFL 2K1, Shenmue

Xbox: Halo, Tony Hawk Pro Skater 2X,

Playstation 2: Rock Band, Guitar Hero, GTA3

Wii: Wii Sports, Mario Kart Wii

XBox 360: Mass Effect Trilogy, Bioshock Ultimate Rapture Edition, Bioshock Infinite

Playstation 3: Catherine, inFamous 2, Final Fantasy 25th Anniversary Ultimate Box

Wii U: Super Mario 3D World, Mario Kart 8, Wind Waker HD

XB1: Gears of War Collection (we all know it is happening), Halo MCC, Sunset Overdrive

PS4: Uncharted Collection, Witcher 3, Batman Arkham Knight

Vita: SAO Hollow Fragment, SAO Lost Song

3DS: Bravely Default, FF Theatrhythm (or however you spell it), Fire Emblem Awakening

PC: Dark Age of Camelot, Age of Empires II, Diablo 2

Edit: as you get further into the generations it gets easier to get multiple games via the collections and remasters :)

PC - Team Fortress 2, Fallout 3, School Mate

NES - Super Mario 3, Legend of Zelda, Mega Man 2

SNES - Earthbound, Chrono Trigger, Super Mario World

N64 - Majora's Mask, Star Fox 64, Super Mario 64

GC - Super Smash Bros Melee, Wind Waker, Paper Mario: TTYD

Wii - Super Mario Galaxy, Twilight Princess, Xenoblade Chronicles

Wii U - SSB4, Mario Kart 8, Zelda U

Genesis - Sonic 2, Mortal Kombat II, Earthworm Jim

PS2 - Kingdom Hearts II, Shadow of the Colossus, Persona 4

X360 - Gears of War, Skyrim, Dark Souls

XB1 - Halo: The Master Chief Collection, GTA V, Halo 5

PS4 - Persona 5, The Nathan Drake Collection, Bloodborne

NES:Mega Man 2,Legend of zelda,super mario bros 3

SNES:A Link to the past, Super Mario world,Super Metroid

N64: Majoras Mask,ocarina of time,Paper Mario

GC:Mario Kart Double Dash,Super Mario sunshine,Super smash bros Melee

Wii: Metroid  Prime trilogy, Twilight Princess,Super Mario Galaxy 1

Wii U: Donkey Kong Country Tropical Freeze,Zelda U, Metroid U (if not metroid comes on Wii U then Xenoblade Chronicles X)

I am really liking some of the choices you guys/girls have put up, and make me realize that those of us who have been fortunate enough to own or play multiple systems since NES era are awesome! I know it's hard to pick even 3 games per system, but figured that it would be better than just 1. Even still, it's tough. In retrospect, SMB 3 should have been on my NES list since it's my favorite SMB game PERIOD because it truly pushed the franchise to the next step.

SNES - Castlevania X, Yoshies Island, Super Mario World

Neo Geo - Pulstar, Metal Slug, Waku Waku 7

PS1 - Yu gi oh Forbidden Memories, Castlevania symphony of the night, Alundra

N64 - Doom 64, Resident Evil 2, Ridge Racer 64

Dreamcast - Last Blade 2, shenmue 1&2

PS2 - Shadow of the collossus, Silent Hill 3, Forbidden Siren 2

Xbox - Metal Gear Solid 2, Silent Hill 2, SVC Chaos

Gamecube - Resident Evil 1, 0, Time splitters future perfect

PSP - Darkstalkers towers, Castlevania X, Blazeblue

Xbox 360 - Last Remnant, Resident Evil 5, Lost planet

PS3 - MGS 4, Siren bloodcurse, Yu Gi Oh Millenium Duels

PSvita - Ridge Racer, Dynasty Warriors, EverBodys Golf

PS4 - Bloodborne, Evil Within, Driveclub

PC - Warcraft 3, Starcraft, Hexen

Wii: Donkey Kong Country Returns, Resident Evil 4: Wii Edition; Metroid Prime Trilogy

Ps3: Metal Gear Solid: The Legacy Collection, Demon's Souls, Jak & Daxter Trilogy

X360: Dark Souls, Gears Of War, Mass Effect Trilogy

XBOX: Timesplitters Future Perfect, Conker Live and Reloaded, Burnout Revenge

GC: Super Smash Bros Melee, Zelda: Wind Waker, Paper Mario TYD

PS2: Final Fantasy X, Ratchet & Clank 2, PES 2005

Dreamcast: Soulcalibur, Dino Crisis, Resident Evil 2

PS1: Tekken 3, Crash Bandicoot 2, Ridge Racer Type 4

N64: Super Mario 64, Mario Kart 64, Starfox 64

SNES: Super Mario World, Super Metroid, Donkey Kong Country 2

Mega drive: Sonic , Sonic 2, Alien Soldier

NES: Super Mario Bros 2, Super Mario Bros 3, Legend Of Zelda

I'll do this for all the systems I currently own plus maybe 1-2 more.

NES - Mega Man 3, Super Mario Bros. 3, Zelda 2.

SNES - A Link to the Past, Super Metroid, Mega Man X3

N64 - Mario 64, OoT, Goldeneye

Gamecube - Melee, Metroid Prime, Twilight Princess

Wii - Super Mario Galaxy 2, Punch-Out, Skyward Sword

Wii U - Mario Kart 8, Super Mario 3D World, Wind Waker HD

360 - Bioshock, Halo 4, Borderlands 2

3DS - A Link Between Worlds, Mario 3D Land, Fire Emblem Awakening

PS1 - Final Fantasy VII, Mega Man X5, MediEvil

PS2 - Metal Gear Solid 3, Final Fantasy X, RE4

PS3 - The Last of Us, Arkham City, Skyrim

Really?  Over Golden Axe 2 (which is obviously the best Golden Axe) and Streets of Rage series?

I had very limited game access back in the Genesis days.  I never played any of the Streets of Rage games.  Golden Axe 2 is probably an oversight, but I went with the first game that wasn't Shining Force that popped into my head.

NES - Mario Bros, Mario Bros 2, Mario Bros 3

Genesis - Mortal Kombat, Sonic 1, Sonic 2

SNES - Super Mario World, Mortal Kombat II, Street Fighter II

Sega CD - Snatcher, Sewer Shark, Popful Mail

Saturn - Virtua Fighter 2, Fighters Mega Mix, Nights

Playstation - Metal Gear Solid, Grandia, Final Fantasy VII

Nintendo 64 - Killer Instinct Gold, WWF No Mercy, Smash Bros

Dreamcast - Shenmue 1, Shenmue 2, Phantasy Star Online

Playstation 2 - Godhand, Metal Solid 2, Metal Gear Solid 3

Xbox - Halo 1, Halo 2, Fable

Xbox 360 - Gears 3, Halo 3, Halo 4

Playstation 3 - Uncharted 2, Uncharted 3, Last of Us