If I had to choose a Mount Rushmore of video game individuals, I don't think you can do just four. You've gotta capture a number of genres, although some are more influential and well known than others...
Shigeru Miyamoto - King of Nintendo, creator of Mario/Link/etc. This is your Action/Platformer representative.
Hironobu Sakaguchi - Creator of the Final Fantasy games, all the good ones anyway. RPG entry here of course. Short of Sakaguchi, I would say Cloud probably fits and is more recognizable.
John Madden - Gotta agree with Woneone here. If you need a figurehead on your mountain to represent Sports games, Madden is probably it. The Madden games changed the genre big time.
Doomguy - This has to be your FPS guy. Master Chief is probably more well known, but not by much and he owes a lot to Doom. Wolfenstein 3D came first (Same company, so not a big deal), but Doom really brought FPS to the mainstream.
Sid Meier - Civilization for RTS genre. There are some RTS games I like more, but Civ is king. Sim City and Age of Empires were there too.
Thrall from World of Warcraft - MMO/MMORPG genre here. Could have gone with one or all of the founders of Blizzard, but I figure Thrall is pretty recognizable. I guess Diablo also works here?
Tetromino - Rather than depict the creators of Tetris, I would put a single Tetromino block for puzzle games.
OutRun Convertible - When I think racing game, OutRun was pretty innovative and you can still find the games in arcades today. Probably could lump Racing in with Sports genre, but I've always separated the two.
Ryu from Street Fighter - Gotta be this for Fighting games.
Minecraft's Steve - Survival. I would also accept Notch, the creator.
PaRappa the Rapper - Now we're talking obscure genres, but there's been a lot of money made in Music/Rhythm games. PaRappa was one of the first templates.
Those cover most genres I think, although there's sub genres and combinations, like MOBAs. If I had to pick 4 for my own personal Rushmore:
Cecil Harvey from Final Fantasy IV
Chosen One from Fallout 2
Little Mac
Darth Vader - Not for any particular game, but more like a representative of all the Star Wars games I've played over the years. My first introduction into flight sims was TIE Fighter, and it also was my first encounter with the Star Wars universe. I hadn't even seen the movies up to that point. That lead to Empire Strikes Back and Return of the Jedi on SNES, Rogue Squadron on 64, X-Wing Alliance, Jedi Knight, Knights of the Old Republic I and II, Star Wars Galaxies (Which I still play), STWOR, Battlefront, Force Unleashed, multiple Lego Star Wars games...the list goes on. When I think about it, I've played more Star Wars games than Mario, Final Fantasy, or any other franchise. They haven't all been winners, but I still play TIE Fighter to this day and love it as much now as I did back then.