The Last of Us and The Last of Us Remastered.

Best story in gaming and a surprisingly good multiplayer.

Super Mario Galaxy ( pinnacle of 3D platforming, I wish it was more open though), Super Mario World ( pinnacle of 2D platforming), Final Fantasy IX ( pinnacle of JRPGs), Paper Mario TTYD (  An amazing game in pretty much every way possible), Resi 4 ( Leaving aside the annoying QTEs this game is perfect) and Counter-Strike ( the grandfather of all competitive shooters)! I wish I could stay here listing all the amazing games that exist, but that would take too long!

Super Mario Absolutely.

GTA Vice City and San Andreas.
Resident Evil 4 and 5
All Tomb Raiders since 2006
Left 4 Dead 1 and 2
Bully
Uncharted 1-3

Why? Because I love playing them, they are all great games providing me with a lot of fun and entertainment.

1: Xenogears
The perfect mech JRPG. The only game I've beaten more than 10 times.
2: Perfect Dark
The best FPS with a female protagonist. Also the best multiplayer on N64.
3: Goldeneye 007
The best Movie Tie-In game ever, and influenced the popularity of shooters on consoles.
4: Resident Evil 4
The best ever Third Person and Survival Horror game I've ever played. Plus, Leon is hot!
5: Xenoblade Chronicles
The best RPG of the 7th generation. Good balance between great gameplay and story that made me ignore the shit graphics.

I'm a huge fan of the Zelda games, nothing else comes close. Was introduced to the series when I was younger by a friend who had Ocarina of Time. I played it, loved it and ended up buying anything that had the Zelda name on it. I might wander away from games at times but I always come back to this series.

Smash Bros. Melee - Spent too long playing this game as a young boy, Ganondorf = wins.

Streets of Rage 2 - Had the absolute best music, no other beat-em-up can touch this (to me anyway). Many of my days were ruined as a wee boy by Mr. X and Shiva, if they hadn't already been ruined by super cheap steroid guy Abadede. Was so happy when I played the BomberGames fangame.

Sonic 3 & Knuckles - I was a SEGA kid growing up, the Genesis/Mega Drive Sonics were untouchable.

Devil May Cry - This is the absolute best of it's genre to me, tied with the original Bayonetta. The music, gameplay, atmosphere, everything about it is perfect.

Bayonetta - Was blown away by how over the top and fun this game was when I first played it, boss fights, music, gameplay, like DMC, everything about it is perfect.

Prince of Persia series - Underrated gems, really wish Ubisoft would shelf the yearly Assassin's Creeds and make another. Spent hours playing through these games.

Ninja Gaiden - Absolute torture, but good torture.

Super Mario Sunshine - Loved this when it came out, I think I lost a few controllers playing it as well.

Luigi's Mansion - This could easily have been a Tim Burton film. Loved the music and the ghosts.

Metroid series - Was a late bloomer with Metroid, absolutely fantastic series.

I approve of your format.

The Legend of Zelda: Ocarina of Time, Majora's Mask, Twilight Princess

Super Mario: 64, 3D World

Super Smash Bros.: 64, Melee

Halo: CE, 4

Perfect Dark: 64, Zero

Dead Space: 1, 2

Mario Kart: 64, DS, 8

Donkey Kong Country: 1, Diddy's Kong Quest

Fire Emblem: 7, The Sacred Stones

F-Zero GX

The Elder Scrolls V: Skyrim

Conker's Bad Fur Day

God of War series (3, 2 & GoS are espeically stunningly good and 1, Asc & CoO are great).
- Best hack 'n' slash series in gaming, perfect balance of story, gameplay, art and music. Closest to prfection.

The Last of Us.
- Amazing characters, story and atmosphere. Moment to moment gameplay is always tense, exciting, rewarding. 

Red Dead Redemption.
- The best sandbox game ever created. A stunning world with great characters, environment is full of life and personality. 

Skyrim.
- An amazingly well crafted game, huge and full of great content. 

Gears of War series (1, 2 & 3)
- Perfected TPS gameplay, great single player adventures with an amazing multiplayer component. 

Alan Wake.
- An amazing story, great setting and some of the best atmosphere in gaming. 

Mass Effect series.
- The best sci-fi saga of all time. Such a rich universe, great story, characters, music, art and gameplay. 

Bioshock series (1 is a masterpiece, 2 & Infinite are also amazing games).
-  The setting, atmoshpere, music, story and gameplay are on point. An amazing series and the best FPS games.

Oddworld AO & AE.
- These are by far the oldest games mentioned, but they hold up beautifully. Stunning artwork, timeless gameplay, superb OST.

Castlevania: Lords of Shadow.
- So underrated it's painful. This game is beautiful, lovely OST, great gameplay and a very good story. An epic, varied and memorable adventure. 

7th Gen (my favorite gen)

Gears of War
Metal Gear Solid
Halo
Uncharted
Forza
Portal
The Elder Scrolls
The Last of Us

6th gen

ICO & Shadow of Colossus
Halo
Conker: Live & Reloaded
Super Smash Bros Melee
Mario Kart Double Dash

5th Gen

Banjo Kazooie
Silicon Valley
Jet Force Gemini
Conker
Paper Mario

4th Gen

Donkey Kong Country
Super Mario Bros