3rd; The Legend of Zelda
4th: The Legend of Zelda A Link to the Past
5th: The Legend of Zelda Ocarina of Time
6th: Metroid Prime
7th: Xenoblade Chronicles

1st: Pong
2nd: Phoenix or Qix
3rd: Super Mario Bros.
4th: Sonic The Hedgehog
5th: Crash Bandicoot 2
6th: Final Fantasy X (all-time favourite)
7th: Heavy Rain

1st: n/a
2nd: Missile Command
3rd: Super Mario Bros. 3
4th: Super Mario World 2: Yoshi's Island (HH: Legend of Zelda: Link's Awakening)
5th: Legend of Zelda: Ocarina of Time
6th: Legend of Zelda: Twilight Princess (HH: Metroid Fusion (played on 3DS))
7th: Uncharted 2: Among Thieves (HH: Professor Layton & Pandora's Box)
8th: -

Sidenote though, the 5th gen contains many of my all time favorites, both on N64 and the PS1. Those games would actually be further up than most 'favorites' from other gens.

This is difficult. As a former computer guy (C64, Amiga and coin-up Arcades for that sake) it's too difficult for me to categorize old games into generations.

1st: Pac-Man
2nd: Bomb Jack
3rd: Conquests of Camelot
4th: Warlords 2
5th: Age of Empires 2
6th: Morrowind
5th: Oblivion
8th: Metal Gear Solid 5

How about that?

Honourable mentions in brackets.

4th - Sonic 2 (Super Mario World)
5th - Syphon Filter (Final Fantasy IX, MGS)
6th - LoZ: The Wind Waker (Luigi's Mansion, Pikmin, SSB Melee)
7th - Super Smash Bros Brawl (Mass Effect 1-3, Dead Space 1-3, COD4, LoZ Skyward Sword & Twilight Princess)

GB - Pokemon Yellow (Tetris, Pokemon Blue/Red)
GBA - Pokemon Ruby/Sapphire (Advance Wars)
DS - Pokemon Diamond
3DS - Kid Icarus: Uprising (Super Mario 3D Land, RE Revelations, Luigi's Mansion 2, MK7, Theathryhtm: Final Fantasy)

4: Kirby Super Star
5: Perfect Dark
6: Metroid Prime
7: Halo Wars

3- SMB is the obvious choice for me but for some reason, I'm really liking Kid Icarus
4-Chrono Trigger with LoZ ALttP close second
5-LoZ OoT or Pokémon Silver
6-Super Smash Bros Melee
7- MAG or Uncharted 2 or Chrono Trigger Ds or Last of Us or Infamous 2 or Red Dead Redemption
8- I only own NSMBU and Nintendoland so I guess the former.

2nd Gen: Asteroids
3rd Gen: River City Ransom
4th Gen: The Legend of Zelda: A Link to the Past
5th Gen: Final Fantasy VIII
6th Gen: God of War
7th Gen: Heavy Rain

3 - SMB3
4 - Super Street fighter 2
5 - Metal Gear Solid/ Half life (PC)
6 - Metroid Prime
7 - Bioshock (original)/ COD MW2 (I know, I know but it was SO ADDICTIVE!)
8 - It was a new Metroid, but now Titan Fall

Gen 3: Sonic the hedgehog 2 (GG)  I wasnt sure wether to include this gen as the only thing i had from the 8 bit era was a game gear.

Gen 4: Sonic 3 & Knuckles
Gen 5: Xenogears
Gen 6: Legacy of Kain Soul reaver 2
Gen 7: Mass Effect 2/3