I see my post in the Video Game Chat thread is influential.
Pong is the most influential game of the 1970's, simply because it's the originator. There were other primitive video games in the 50's and 60's, but they were only available on massive computers at universities and government facilities. Pong was the first video game to be commercially available to the public.
For the 1980's, I stand by The Legend of Zelda being the most important or influential game of the decade because it was a lot more plot-oriented than other NES games and was one of the first games to make a big deal out of saving your progress and it was a major influence on the open-world and RPG genres of gaming. Super Mario Brothers is also noteworthy, but I'd say Zelda is more important in the grand scheme of things.
The 1990's is the hardest decade to pick a single "most influential game" for, because so many genres and overall aspects of video games as a hobby either started in the 1990's or greatly proliferated then.
I'm going with Doom simply because it codified the FPS genre and was probably the first mainstream video game to have a very active modding and online multiplayer scene, but you could also make the argument for Street Fighter II or Metal Gear Solid being the most influential game of the 90's.
With the 2000's, Grand Theft Auto III is a no-brainer choice. Even if GTA III was simply an evolution of preexisting trends and Rockstar happened to be the first to the punch, it's still the game that made open world games into a full-fledged genre. Open-world games existed before GTA III, but they weren't really a true codified genre. Games like Driver and Body Harvest were like the Wolfenstein 3D to GTA III's Doom.
The 2010's, I'm also going with Minecraft, even if it technically came out in the tail end of 2009.
