Crash Bandicoot. THE Playstation 1 mascot and 2.5 platforming. Probably one of the most iconic gaming mascots

The Last of Us. A landmark of cinematic storytelling

Ratchet and Clank because it's the greatest gaming franchise ever

God of War

Metal Gear Solid 3 for being the greatest story ever told in any medium

I'm sure Kingdom Hearts will make it one day.

 Have you played Street Fighter?  It kind of sucks.  Street Fighter 2 took very little from it.

Here's a few I think should be inducted in the future:

RTS

-Age of Empires should probably make the list eventually... everyone seems to have played it. My cousin (grew up in Puerto Rico, been living in Netherlands for a few years) recently visited and he said he and his friends used to play it too, so evidently it was not merely a NA thing.

-Starcraft is probably very deserving for its cultural impact... I think more than any game Starcraft really got the whole "professional gamers" thing started when those tournaments were literally televised as a big event in South Korea.

-Warcraft III...ish, as the Bonus campaign from the Warcraft III expansion largely gave birth to an entire new genre in the MOBA, but I imagine they'd pick the mod or first games for that instead.

Arcade

-Galaga: While taking a ton of inspiration from Space Invaders and Galaxian, this one really got the "shoot 'em up" genre started

-Ms. Pac-man might be worthy of an eventual addition simply because it featured a female protagonist and was an all around improvement upon Pac-Man

RPG

-Dragon Warrior: It seems weird to me that neither this nor Final Fantasy are in the Hall of Fame yet; one certainly ought to be, and given this came first I'd opt for it

Early 3D Games (Fifth Gen)

It seems odd to me that this era is mostly being ignored, but I imagine that's because it has aged worse than just about any generation. That said, those games which were able to show everyone else how to make that difficult transition into 3D deserve credit for doing so... the obvious three that leap to my mind are Mario 64, Zelda OoT, and Final Fantasy VII.

I easily second Galaga

Galaga is probably one of the most recognized arcade games of all time and really did practically single handedly build the scrolling ship shooter genre on its own (and much more so than its sister game Galaxian IMO).

practically anyone recognizes the Galaga ship, there have been like 50 compilations including it over the decades (because its a hugely popular game through generations), and to this day (despite SO many arcade shooters having chances to improve upon the format) Galaga is still one of most balanced and pure arcade shooters around.

Incredibly replayable regardless of age and literally THE game that popularized a genre and debatably Galaga played a huge part in the arcade movement in the 80s and 90s (with a Galaga machine being in like every bar everrr)

Its a masterpiece. At minimum I hope it has been in the selections rounds as a choice 

It was my arcade cabinet of choice on the fairly rare occasions that I got to go somewhere with a lot of them. I think it might feature one of the first "secrets" (though exceedingly easy to discover) that many people would encounter in that anyone who played the game would almost certainly do that "get two ships" trick on accident. It blew my mind and I just remember instantly loving the game the moment that happened lol