3rd - Super Mario Bros.

4th - Super Mario Kart (I guess. Haven't played that many games from this generation.)

5th - The Legend of Zelda: Ocarina of Time

6th - F-Zero GX

7th - Halo 3

8th - Mario Kart 7

Missile Command, Donkey Kong Jr., and Centipede

Final Fantasy and Dragon Warrior(Series)

7th Saga and Top Gear

Shining the Holy Ark, Shining Force 3, Legend of Zelda OOT, and Persona series

Shin Megami Tensei(All), Super Mario Sunshine, Sonic Adventure, NFL 2Kand 2K1, Skies of Arcadia, Grandia 2, and Romance of the Three Kingdoms

5th - Spyro: Year of the Dragon (Special mention: Final Fantasy VIII)
6th - Pikmin (Special mention: SSX 3)
7th - Ratchet & Clank: A Crack in Time (Special mention: LittleBigPlanet)

Overall special mention: World of Warcraft (I have no idea what generation this would be in :P)

Haven't really played enough games from other generations to comment on them.

1st and 2nd generation before my time.
3rd generation- only played 2 games, Super Mario Bros and Duck hunt on NES so i shouldn't pick one from there
4th generation- Super Mario World (SNES)
5th generation- Syphon Filter (PS1) and Mario Kart 64 (N64)
6th generation- GTA san andreas (PS2) and Chu Chu Rocket! (Dreamcast)
7th generation- Uncharted 2/ Red Dead Redemption (PS3) and Super Mario Galaxy (wii)

Handhelds

Game Boy- Tetris/ Super mario land 2
Game Boy Advance- Any of the Mario or Sonic re-releases
PSP- GTA Liberty City Stories
Vita (so far)- Uncharted golden abyss

3rd Gen
Super Mario Bros 3

4th Gen
Link to the Past

5th Gen
Banjo Kazooie

6th Gen
Halo 2

7th Gen
Gears of War/metal Gear Solid 4

4th gen - super mario world
5th gen - super mario 64
6th gen - God of war 2
7th gen - impossible to chose, either RDR, KZ2, GOW3 or TLoU

Top 10-15 from each gen. With some notable games included. (My personal List) Hence loads of wrestling aha)

3rd:

1. Wonderboy 3: The Dragons Trap (SMS)

2. Golvellius (SMS)

3. Golden Axe Warrior (SMS)

4. Mario Series (NES)

5. New Zealand Story (SMS version)

6. Land of Illusion (SMS)

7. Alex the Kidd in Miracle World (SMS)

8. Bubble Bobble (SMS version)

9. Zelda (NES)

10. Gremlins 2 (NES)

4th:

1. Chronno Trigger (SNES)

2. Wardner (MegaDrive)

3. Wonder Boy in Monsters World (MegaDrive)

4. illusion of Time (SNES)

5. The Lion King (MegaDrive Version, snes has horrible resolution)

6. Sonic Series (MegaDrive)

7. Streets of Rage Series (MegaDrive)

8. Catle of illusion (MegaDrive)

9. Final Fantasy 3/6 (SNES)

10. Golden Axe Series (MegaDrive)

11. Zelda a link to the past (SNES)

12. Alladdin (MegaDrive Version)

13. Mario Series (not including paper mario/mario rpg/mario party) (SNES)

14. Soliel (MegaDrive)

15. Donkey Kong Series (SNES)

Honrable Mensions: Zombies ate my neighbours, Mortal Kombat, Road Rash series, Street Fighter series, Contra: Probotector, Super bomberman, Legend of a mystical ninja, Castlevania: The New Generation, Killer Instinct

5th

1. Crash series (PS1)

2. Wrestling games. (PS1/N64)

3. Spyro Series (PS1)

4. Zelda Series (N64)

5. Tenchu Series (PS1)

6. Command and Conquer Series (PS1)

7. Tekken 3 (PS1)

8. Grandia (PS1)

9. Mario 64/Kart (N64)

10. Harry Potter (PS1)

Honrable Mentions: Tomb Raider Series,  Metal Gear Solid , Theme series park/hospital, Bloody Roar, Residemt Evil, 007: Golden Eye.

6th

 1. Jak n Daxter Series (PS2)

2. Crash Bandicoot: Wrath of Cortex (PS2)

3. God of War Series (PS2)

4. Smackdown Series (PS2)

5. Mortal Kombat Series (PS2)

6. Shenmue Series (DC)

7. Luigis Mansion (GC)

8. Harry Potter Series (PS2)

9. Gran Tursimo Series (PS2)

10. Kingdom Hearts Series (PS2)

11. Zelda Twilight Princes (GC)

12. Fable Series (XBOX)

13. Need For Speed Underground 2

14. Grandia 2 (DC)

15. Final Fantasy Series (Number 11 drags it down) (PS2)

Honrable Mentions: Tekken Series, Tony Hawks Series, GTA Series

7th

1. The Last of US (PS3)

2. Uncharted Series (PS3)

3. Metal Gear Solid 4 (PS3)

4. God of War Series (PS3)

5. Gran Turismo 5 (PS3)

6. New Super Mario Bros Wii (Wii)

7. Mortal Kombat (PS360)

8. Killzone Series (PS3)

9. Donkey Kong Country Returns (Wii)

10. Red Dead Redemption (PS360)

11. Valkyria Chronicles (PS3)

12. Heavy Rain (PS3)

13. Just Dance Series (Wii)

14. Ratchet and Clank future: A Crack in Time (PS3)

15. Street Fighter Series (PS360)

Iam sure i am missing one ot two good games because i listed these off my head.

Gen 1, 2, and 3: Before my time

Gen4: Sonic The Hedgehog (Genesis)

Gen5: Resident Evil 2 (Multi-plat)

Gen6: Pikmin 2 (Game Cube)

Gen7: Super Smash Bros Brawl (Wii)

Gen8: Animal Crossing New Leaf (3DS) (So far)

First gen: Missed.
Second Gen: Pitfall (Atari)
3rd Gen: Super Mario 3, Super C, Die Hard, Bart vs the space mutants, Super Mario Bros 2. (NES)
4th gen: Chrono Trigger, Legend of Zelda, Flashback, Out of this World (SNES)
5th gen: Legend of Legaia, Silent Hill, Metal gear solid, Resident Evil 2, Gran Turismo, Final Fantasy 8 (Playstation)
6th gen: Silent Hill 2, Silent Hill 3, Silent Hill 4, Fatal Frame 1-2-3, Metal Gear solid 2-3 (PS2).
7th gen: The last of Us, Uncharted 2, Heavy Rain, Valkyria Chronicles, Metal Gear Solid 4 (PS3).

1st-4th gen: Can't remember much. lol!
5th gen: Sakura Taisen (Genesis) / Suikoden (PS1)
6th gen: Shenmue (Dreamcast) / Persona 4 (PS2)
7th gen: Valkyria Chronicles (PS3) / Lost Odyssey (360) / Xenoblade (Wii)
8th gen: TBD