darkSpyro

For me:
NES - Mega Man 2
SNES - Super Mario World
N64 - Paper Mario
GC - Paper Mario: The Thousand Year Door
Wii - Super Mario Galaxy
Wii U - Super Smash Bros. for Wii U
GB - Pokémon Blue Version
GBC - Shantae
GBA - Pokémon Emerald Version
DS - Pokémon Soul Silver Version
3DS - Fire Emblem: Awakening

NES - The Legend of Zelda
SNES - idk
N64 - The Legend of Zelda: Majora's Mask
GC - The Legend of Zelda: Wind Waker
Wii - Xenoblade Chronicles
Wii U - Splatoon
GB - Pokémon Yellow Version
GBC - idk
GBA - Pokémon Emerald Version
DS - Pokémon Diamond Version
3DS - Fire Emblem: Awakening

im gonna skip nes, snes, gameboy, and gameboy color for now because i havent played a lot of games for them and it's all been virtual console anyway

N64 - Super Mario 64 (it was the first video game I ever played, too)
GameCube - Either Pokemon Colosseum, or Mario Kart Double Dash!! or Metroid Prime 2: Echoes (but Echoes suffers in my eyes because I hate the GameCube controls for it)
GameBoy Advance - Metroid Fusion (Pokemon Emerald is a close second)
Wii - The Legend of Zelda: Skyward Sword or Metroid Prime 3: Corruption
DS - Pokemon Black
Wii U - Splatoon
3DS - Pokemon AlphaSapphire

NES: Super Mario Bros. First game I ever played.
SNES: Either Super Mario World or Star Fox. And if it counts, the unreleased Star Fox 2 is probably even better than both games, so I guess it's my overall favourite.
Game Boy/Colour: The Legend Of Zelda: Link's Awakening DX, Kirby's Dreamland, and Super Mario Bros. Deluxe.
N64: Super Smash Bros
GameCube: Star Fox: Assault
GBA: The Legend Of Zelda: The Minish Cap
Wii: Super Mario Galaxy and it's sequel, Kirby's Return to Dreamland and SSBB
DS: Super Mario 64 DS, and Kirby Super Star Ultra
Wii U: Super Smash Bros. for Wii U. Besides that, Super Mario 3D World, Hyrule Warriors, and Captain Toad: Treasure Tracker are all games I adore.
3DS: Kid Icarus: Uprising, Kirby Triple Deluxe, and Luigi's Mansion 2

NOTE: I was assuming the OP meant only games that use first party Nintendo IPs, so other games like Sonic games and Mega Man games are not included even if I really like them.

I'm only going to do the systems I own and I'm going to list 4

GameCube: MarioKart DoubleDash/ Paper Mario: The Thousand Year Door/ Sonic Adventure 2 Battle/ Shadow the HedgeHog
Wii: MarioKart Wii/ Skylanders Giants/ Mario Super Sluggers/ Just Dance 2
Wii U: Super Smash Bros/ Hyrule Warriors/MarioKart 8/ and I know I'm going to love it: Super Mario Maker
DS: MarioKart DS/ Super Mario 64 DS/ Lego Harry Potter Years 5-7/ Mario Party DS
3DS:Super Smash Bros/ Puzzles & Dragons Z/ MarioKart 7/ Lego Lord of the Rings

I don't have any overall favorites for recent consoles so I may list more than one.

NES: Final Fantasy

SNES: Super Mario World, Earthbound

GB/C: Pokemon Gold

N64: Yoshi's Story and Super Mario 64

Gamecube: Super Mario Sunshine, Super Mario Strikers, Naruto Clash of Ninja 2, Super Smash Bros Melee, and Tales of Symphonia (if I had to chose from all 5, it would be Tales of Symphonia though)

GBA: (Ok so I emulated quite a bit of these games, so let me just start from games I own/ed.) Mario and Luigi: Superstar Saga, Pokemon FireRed, Pokemon Sapphire, F-Zero Maximum Velocity (3DS), Fire Emblem: The Sacred Stones (3DS), Metroid Fusion (3DS), Legend of Zelda: Minish Cap (3DS). For emulated, Pokemon Emerald, Kingdom Hearts: Chain of Memories.

Wii: Super Mario Galaxy 1 and 2, Xenoblade Chronicles, Legend of Zelda: Skyward Sword, Wii Sports Resort, Okami, Metroid: Other M, Metroid Prime Trilogy.

DS: Pokemon Diamond, Pearl, Platinum, HeartGold, SoulSilver, Black/2, White/2. Mario and Luigi: Bowser's Inside Story, Legend of Zelda: Phantom Hourglass, Legend of Zelda: Spirit Tracks, Pokemon Ranger/:Shadows of Almia/:Guardian Signs, Final Fantasy: Four Heroes of Light, Rhythm Heaven, Kingdom Hearts 358/2 Days, Inazuma Eleven 2: Ice.

Wii U: Legend of Zelda: Wind Waker HD, Super Mario 3D World, Wii Sports Club, Monster Hunter 3 Ultimate, Smash Bros Wii U, Hyrule Warriors, Splatoon, Mario Kart 8.

3DS: Bravely Default, Fire Emblem: Awakening, Shin Megami Tensei IV, Persona Q, Etrian Odyssey Untold, Kingdom Hearts 3D, Smash Bros, Kid Icarus Uprising, Animal Crossing New Leaf, Professor Layton and the Miracle Mask, Phoenix Wright: Ace Attorney: Dual Destinies, Rune Factory 4. (just to name the few)

NES: Mega Man 1

SNES: Mega Man X

GB/C/A: ????

Wii: Super Mario Galaxy 1 and 2

DS: Animal Crossing Wild World, and yes, Go Diego Go Dino Hunters. Not even joking this game is 10/10.

Wii U: Well, it isn't out yet, but Zelda Wii U just from trailers. Otherwise, it would have to be Smash.

3DS: Smash and Animal Crossing New Leaf

NES/SNES: Super Mario Bros., Donkey Kong Country, Donkey Kong Country 2

GB/C: Pokemon Blue, Pokemon Silver, Pokemon Crystal, Shrek Fairytale Freakdown

N64: Pokemon Stadium, Pokemon Stadium 2, Super Smash Bros., Mario Kart 64, Pokemon Snap

GameCube: Super Smash Bros. Melee, Pokemon Colosseum, Pokemon Gale of Darkness, Mario Kart Double Dash, Mario Party 4 & 5, Super Mario Strikers, Star Fox Assault, Pikmin, Sonic Adventure DX, Sonic Adventure 2 Battle, Sonic Heroes, Sonic Riders, Shadow the Hedgehog, Ty the Tasmanian Tiger, Ty the Tasmanian Tiger 2 Bush Rescue, Teenage Mutant Ninja Turtles, TMNT 2 Battle Nexus, TMNT 3 Mutant Nightmare, Dragon Ball Z Budokai, Dragon Ball Z Budokai 2

GBA: Sonic Advance, Sonic Advance 2, Sonic Advance 3, Sonic Battle, Pokemon Sapphire, Pokemon Emerald, Pokemon FireRed, Pokemon LeafGreen, Wario Land 4, Donkey Kong Country 3, Super Mario Advance, Dragon Ball Z Buu's Fury, Yu-Gi-Oh! The Eternal Duelist Soul, Kirby & the Amazing Mirror

Wii: Super Smash Bros. Brawl, TMNT Smash Up, New Super Mario Bros. Wii, Skylanders Giants, Sonic & Sega All-Stars Racing, Sonic Unleashed, Mario Kart Wii, Animal Crossing City Folk

DS: Pokemon Diamond, Peal, Platinum, HeartGold, SoulSilver, Black/2, White/2, Mario Kart DS, Sonic Rush, Mario Hoops 3 on 3, Pokemon Mystery Dungeon Blue Rescue Team, Explorers of Time, Explorers of Darkness, Explorers of Sky, Chrono Trigger, Kirby Super Star Ultra, Kirby Squeak Squad, New Super Mario Bros., Sonic Colors, Super Mario 64 DS

Wii U: Super Smash Bros. Wii U, Skylanders Trap Team, New Super Mario Bros. + New Super Luigi U, Rayman Legends

3DS: Super Smash Bros. 3DS, Pokemon Omega Ruby, Alpha Sapphire, X, Y, Mario Kart 7, Sonic Generations, Animal Crossing New Leaf

NES - Super Mario Bros. 3
N64 - Banjo-Kazooie
GC - Super Mario Sunshine
Wii - Super Mario Galaxy (dunno which one of them)
Wii U - Mario Kart 8
GBA - Banjo-Kazooie: Grunty's Revenge
DS - Super Mario 64 DS
3DS - Pokemon AlphaSapphire

Haven't played much from the other systems so.

I only have two Nintendo consoles, so I'm listing my top three

Wii
1: Super Mario Galaxy
2: Super Mario Galaxy 2
3: I haven't played any other games recently... I'm just going to put Skylanders: Swap Force. (I haven't played any Skylanders games since I lost my Kaos Trap. Yep, sore loser, I know.)

Nintendo DS

1: Spyro: Shadow Legacy
2: New Yoshi's Island
3: (Not saying it. I'm going to get laughed out of the forums.)

NES: Duck Hunt
SNES: The Legend of Zelda: A Link to the Past/Megaman X
GB/C: Super Mario Land 2- 6 Golden Coins/Shantae
N64: none
GameCube: F-Zero GX
GBA: Mario and Luigi: Superstar Saga
DS: Pokemon Diamond/Pearl/Platinum
Wii: Kirby's Return to Dreamland/Sonic Colors
3DS: Pokemon Omega Ruby/Alpha Sapphire
Wii U: Super Smash Bros. for Wii U

NES: Super Mario Bros
SNES: The Legend of Zelda: A Link to the Past
GB/C: Pokemon Crystal
N64: Banjo-Tooie
GameCube: Super Mario Sunshine
GBA: Mario and Luigi: Superstar Saga
DS: Mario Kart DS
Wii: Galaxy 2
3DS: Pokemon Alpha Sapphire
Wii U: Super Mario 3D World

NES: Megaman 2
SNES: Super Mario World
GB/C: Pokemon Gold
N64: Pokemon Stadium/ Super Mario 64
GameCube: SSBM/ POkemon Coliseum
GBA: Pokemon Emerald
DS: Mario Kart DS/ Pokemon BW 2
Wii: SSBB
3DS: Fire Emblem Awakening
Wii U: SSB4