I'll also just go with the ones listed by the OP:

Final Fantasy - FF6. The 1st one I played and the most enjoyable as well. It's just one of those games that define the greatness that was the 16 bit era. Excellent presentation and sound, great characters, and just a blast to play.

Mario - probably Sunshine. I love Mario 64, but I feel Sunshine just improves on it, makes for a cool, tight Mario with the cool extra mechanics of FLUDD as well. :D

Zelda - Majora's Mask. The most memorable and enjoyable Zelda game for me. I would talk with my friend about it at school everyday, updating each other on our progress and just discussing things we encountered on our playthroughs. Also, the most unique and interest Zelda game.

Pokemon - Silver. It still remains for me the highest point of the series, with the most improvements and new features added to the series. After this game, the series fell back down to a default point, slowly climbing back up, but still not reaching the high point that Silver/Gold brought to the series.

Mario: Paper Mario: The Thousand Year Door
Pokemon: Crystal
Zelda: Breath of the Wild
Final Fantasy: VI
Metroid: Super Metroid
Fire Emblem: Radiant Dawn
Dragon Quest: VI
Persona: 4 Golden
Assassin's Creed : II

MGS- MGS3

The most complete MGS story. Incredibly well written and told. The twists serve as both innovations and callbacks. The perfect Video Game.

Final Fantasy: FF7. Nuff Said.

Pokemon Sun
Pokemon black and white and black/white 2
Uncharted 2
Super Mario Bros.
Gran turismo 3
GTA V

Metal Gear Solid - Snake Eater
Bioshock - Infinite
Pokemon - Fire Red
Zelda - Wind Waker
Megaman - Battle Network 6
Grand Theft Auto - San Andreas
Soulsborne - Bloodborne
Dragon Age - Inquisition

Metroid prime 2

Super Mario Sunshine

Zelda skyward sword

Kirby 64

Batman Arkham City

GTA San Andreas

Resident Evil 4

Crash Bandicoot 3

Persona 4 Golden
Pokemon Silver
Mario Galaxy 2
Harvest Moon: Back the Nature
The Legend of Zelda: Wind Waker ( i didnt played BotW yet )
Metal Gear Solid 4: Guns of the Patriots
The Witcher 3: Wild Hunt
Final Fantasy X
Fire Emblem: Awakening
God of War 3

Super Mario Galaxy
Wind Waker ( not done with BoTW)
Metroid Prime
Resident Evil 4
Final Fantasy IX

Tekken - 5, it's just the best Tekken made so far. Then 3.
Final Fantasy - 7 because it was my first (don't think it's the best though).
Zelda - of those I've played Wind Waker, loved it.
Mario - Galaxy, modern Mario and unique idea.
Crash - 2, so good. 3 didn't seem right to me... I mean apple cannons? and Polar Bear beats tiger.

Not sure about other series. Wipeout 2097, maybe...

It's a close call, but it's like Tekken 5 is just a more rounded smoother more modern version of 3. Plus you had costumes so could make characters look stupid.... I know, lack of Gon and Dr Bosconovitch hurts it. 6 ruined things by the bound/juggling stuff.

this said, when I wrote that I forgot about Tag.... Tag was pretty awesome if just because it had bowling, like 5 did on the PSP.

EDIT: Oh and a fight? How does June 2nd sound?