You know when there's that one game that becomes almost synonymous with a given video game system, where it's the first game that springs to mind when you think of that system and vice versa, where the game becomes an icon for that console?

What are some of yours?

NES - Super Mario Bros. 3

SNES - Super Mario World

N64 - Super Smash Bros.

PS1 - Crash Bandicoot 3

PS2 - God of War II

GC - Luigi's Mansion

3DS - Mario Kart 7

Wii - Super Smash Bros. Brawl

WiiU - Super Mario 3D World (Or Mario Kart 8, not sure)

Most of those were the first games I played on the system, so that's why I relate.

For me it’s a tossup between Super Mario 64 on N64 or Halo: Combat Evolved for Xbox in terms of most iconic standout titles that defined their respective platforms.

NES - The Legend of Zelda

SNES - A Link to the Past

N64 - Super Mario 64

GC - Twilight Princess

Wii - Wii Sports

Wii U - Bayonetta 2

Switch - Breath of the Wild

PS1 - Final Fantasy VII

PS2 - Dragon Quest VIII

PS3 - Valkyria Chronicles

PS4 - Persona 5

Xbox 360 - Halo 3

Genesis - Sonic the Hedgehog

Saturn - Panzer Dragoon Saga

Dreamcast - SoulCalibur

Atari 2600 - Yars' Revenge

Game Boy - Pokemon Red/Blue

GBA - Mother 3

DS - Dragon Quest V

3DS - Fire Emblem Awakening

PSP - Crisis Core

PS Vita - Persona 4 Golden

NES - Super Mario Bros 3
Gameboy - Mystic Quest
Mega Drive - Sonic 2 
SNES - SimCity and Donkey Kong Country (even though I like the major RPGs more - FF4 was a really special one as it cost me my childhood life savings to import it and remains the most expensive game I ever bought, before inflation, to this day)
PSX - Xenogears
N64 - Goldeneye 007
Dreamcast - Skies of Arcadia
PS2 - GTA Vice City
GBA - FF4 Advance
DS - Dragon Quest 5, 9, and the Ace Attorney trilogy
Wii - Xenoblade Chronicles, Galaxy, or Virtual Console
PS3 - Assassin’s Creed 2
3DS - Mario Kart 7
Vita - Xenogears
Wii U - Xenoblade Chronicles X
Switch - Breath of the Wild, Mario Kart 8, and Witcher 3

Dreamcast-Shenmue
Saturn-Radiant Silvergun
Genesis/Mega Drive-MUSHA
TurboGrafx/PCE-CD-Ys

PS1: Gran Turismo
PS2: Final Fantasy X
PS3: The Last of Us
PS4: God of War
PS5: TBD
Xbox: Halo CE
Xbox 360: Halo 3
Xbox One: N/A
Xbox S/X: TBD
Gameboy: Pokemon Red
N64: Mario Kart 64
3DS: SMT Devil Survivor Overclocked
Switch: Xenoblade Chronicles 1-3

(only including systems I played)

Xbox: Halo
Xbox 360: Gears of War
Xbox One: Killer Instinct
Xbox Series: TBD

Genesis Sonic the hedgehog 2

I take it the OP is asking which games are most synonymous/famously associated with the system, not which games you think are "best" or are your personal favorite (like Xenoblade on the Switch ... c'mon, lol). 

NES - Super Mario Bros.
Game Boy - Tetris
Genesis - Sonic the Hedgehog
Super NES - Street Fighter 2
N64 - Super Mario 64 or GoldenEye 007
Playstation - Final Fantasy VII

PS2 - GTA3
GameCube - Super Smash Bros. Melee
GBA - Mario Kart Super Circuit
XBox - Halo
XBox 360 - Call of Duty: Modern Warfare
PSP - Ridge Racer (Monster Hunter in Japan)
DS - Brain Training
Wii - Wii Sports or Mario Kart Wii
PS3 - Uncharted 2
3DS - Super Mario 3D Land
XBox One - Forza
PS4 - Last of Us Part II
Wii U - Splatoon
Switch: Zelda: Breath of the Wild

Dreamcast - Soul Calibur

Saturn - NiGHTS (I guess?)

Atari 2600 - Pac-Man

Turbo Grafx 16 - Bonk's Adventure