I'm eager to know :P

Mario because Mario. Zelda because Zelda. Final Fantasy because Final Fantasy. Aside from those 3, it's hard to find a franchise with such an extensive legacy... How did they achieved that? By being quality games, staying relevant for decades, innovating and being the best of their respective genres for so long, and because of the brands they have become.

No God of War, No Halo, No Uncharted, No Sonic, etc. They're far from having the legacy the ones I mentioned have.

Pokemon, Street Fighter, Castlevania... They come to mind as well. But I guess they don't have as much legacy and history.

HALO 2. The online shooter. It was ground breaking at the time. It made FPS what it is today and what online play is today.

Zelda definitely, as it was the template for so many games that came after. Final Fantasy definitely. I can still remember loving FF1 on the NES, how it felt so different from other games of that era. Elder Scrolls for more adult oriented fantasy. ICO/SotC, for its elegance and emotion and all the influence it has had on the industry. Half Life, for good storytelling combined with FPP. CoD for blowing up the popularity of FPS competitive multi-player. WoW for simply bulldozing the MMO genre.

Final Fantasy.

Metal Gear Solid.

Aside from the obvious choices, Wolfenstein, hands down, it was the FIRST FPS ever, it paved the way for one of the largest genres currently found within the video game industry. Without this game the modern FPS wouldn't be the same.

Mario - defined platforming, even 3D platforming
Zelda - classic adventuring for young and old
Goldeneye - pioneered multiplayer FPS games
Final Fantasy - name is synonymous with rpgs
Dragon Quest - but only in Japan really

Um... all i can think of off the top of my head.

God of War, Gran Turismo, The Elder Scrolls, GTA, Mario, Halo, CoD... Pretty much every franchise that are at the top of their genre critically and/or commercially.

Anything other than Mario is incorrect ...