PS1: Gran Turismo 2
PS2: God of War 2
PS3: God of War 3

PS4: Infamous: Second Son

PSP: God of War: Ghost of Sparta

Xbox: Halo 2
Xbox 360: Forza Horizon

GBA: Pokemon Emerald

DS: GTA Chinatown Wars

PS1 Crash Bandicoot 3 Warped
PS2 WWE Smackdown Here Comes the Pain
PS3 Uncharted 2 Among Thieves
PSP Ridge Racers
PSV Uncharted Golden Abyss

NES Super Mario Bros.
SNES The Legend of Zelda A Link to the Past
N64 Mario Kart 64
Gamecube Super Smash Bros. Melee
Wii Super Mario Galaxy 2
GB Pokemon Silver
DS Mario Kart DS
3DS Super Mario 3D Land

From the systems i own

PC - Warcraft 3

PS4 - Bloodborne
PS3 - Siren Bloodcurse
PS2 - Forbidden Siren 2
PS1 - Alundra
PSvita -Freedom Wars?
PSP - Ridge Racer? not into handhelds

Wii U - Project zero Maiden of Blackwater
N64 - Doom 64
SNES - Super Mario World 2: Yoshies Island (tough i think this was ported to many other systems)

Xbox - Panzer Dragoon Orta

Dreamcast - Shenmue
Sega Saturn - Keio 2

Neo Geo - Pulstar (dont own the game, from the games i own its Waku Waku 7)

it does count it even had mouse and keyboard support and run pretty smooth on consoles

Yeah meant Cortex Strikes back xD, i always mix up the title for that game.

Interesting question, though I'm not entirely satisfied with my answers:

Microsoft:

- Halo 2 (OG Xbox)

- Dead Rising (Xbox 360). If this one doesn't count since it got re-released a few days ago everywhere, then Fable 2.

Sony:

- Soul Blade (PS1)

- ICO (Ps2)

- Infamous 2 (PS3)

- Bloodborne (PS4)

Nintendo:

- Super Mario 64 (Nintendo 64)

- The legend of Zelda: Wind Waker (Gamecube)

- The Last Story (Wii)

- Smash Bros U. (WiiU)

- Hotel Dusk: Room 215 (NDS)

- Fire Emblem: Awakening (3DS)

Nintendo -
SNES: The Legend of Zelda: A Link to the Past
Gameboy: Pokemon (Blue/Red)
N64: Goldeneye
Gamecube: The Legend of Zelda: Wind Waker
NDS: New Super Mario Bros.

SEGA -
Megadrive (Genesis): Sonic 2
Dreamcast: Jet Set Radio


Microsoft -
Xbox: Halo: Combat Evolved
Xbox 360: The Lost Odyssey


Sony -
PS1: Final Fantasy VIII
PS2: Timesplitters
PS3: Uncharted 2: Among Thieves            PSP: God of War Chains of Olympus
PS4: Uncharted 4: A Thief's End - so far

PC -
Age of Mythology

I don't recognize "true" exclusives. If a game is not on PS4 and Wii U but on Xbox One, it's an exclusive weather it's on PC or not. PC does not compete consoles. I also count timed exclusives as exclusives because for a year or more, when the game was being consumed at it's highest point, it was only on one console.

NES - SMB3
SNES - DKC 1
Genesis - Sonic 2
Sega Cd - Dracula Unleashed
Saturn - Nights Into Dreams
PS1 - Resident Evil 1
N64 - OOT
Dreamcast - Resident Evil CV
PS2 - GTA 3
Xbox - Halo 2
Gamecube - Animal Crossing
Xbox 360 - Halo 3
PS3 - Uncharted 2
Wii - Wii Sports
PS4 - Infamous SS
Xbox One - Halo MCC
Wii U - Splatoon


Gameboy - Tetris
Gameboy Color - Zelda Oracle of Ages
GBA - Castlevania COTM
PSP - Lumines
DS - Meteos 
3DS - Animal Crossing New Leaf

SNES - EarthBound
N64 - The Legend of Zelda: Ocarina of Time
Wii - The Legend of Zelda: Skyward Sword
Wii U - Bayonetta 2

GBC - Pokémon Gold
NDS - Pokémon Platinum
3DS - The Legend of Zelda: A Link Between Worlds

Bonus platforms:

PS1 - Crash Bandicoot: Warped
PC - The Sims 2

Honorable Mentions:

(N64) Super Mario 64, The Legend of Zelda: Majora's Mask

(Wii) Super Mario Galaxy, Super Paper Mario

(Wii U) Splatoon, Super Smash Bros.

That's fine, but I'm sure you're aware that most of your last just simply won't count