Super Mario Bros: Needs little explanation, it popularized the platform genre beyond anything before or since and has left its mark in a thousand different ways and even across genres and introduced several revolutionary concepts.
Tetris: Started a whole genre on its own and was the founding father of what is now objectively the largest genre of games in the world by far, games following in this titles footsteps have reached sales/downloads in the billion territory (Bejeweled) and continue to grow in popularity and diversity (Tetris, in hindsight, probably ruined my mother's life... 
).
Street Fighter: The big one that started it all, there is not a single beat 'em up title today that doesn't share DNA with this amazing franchise.
Doom: Wolfenstein may have started the modern FPS, along with the likes of Blake Stone, but Doom sent it soaring into the gaming skies and can easily be said to be the main influence of the highest grossing genre in modern gaming, no mean feat!
Ultima series: Games such as Ultima Underworld are doubtless to thank for open world and sandbox titles with deeper mechanics becoming what they are today in all their glory.
Fallout: The original, it broke so much ground on so many levels, first and foremost in mature narratives and heavy subjects that no one dared touch before this title but also in interface solutions and turn-based isometric gaming in general.
Pokemon: The best selling video game franchise in the world by far and inspiration for dozens of similar concepts, it has become a phenomenon that not only sells gazillions of effects and software and movies but has also struck a chord with a global audience, something very few gaming concepts manages.
Civilization: The father of the expanded scope in strategy games, it had deeper mechanics and featured the whole actual world to tinker with and is the basis on which almost all turn-based strategy is built today in some form or other.
Half-Life: The very epitome of pacing and narration in FPS games and also the first shooter to feature AI that actually tried to resist in a somewhat meaningful way by flanking, using hand grenades and communicating between them in combat. And, as we all know, the sequel revolutionized FPS gameplay by making real-world physics a part of the game as well.
Deus Ex: The first true master of branching storytelling and morally ambiguous choices with actual effect on gameplay and the game world, it was also the first truly successful merger of several gameplay concepts, fusing stealth, hacking, weapon upgrades, potential non-lethal and RPG elements in upgrading your arsenal as well as your character with more classic FPS gameplay.
Farmville: As much a waste of space and time I feel that this game is; it is undeniably the very start of the rockslide that would become the social and browser-based gaming arena and it was at the forefront of what has become a ridiculously popular segment of gaming today.
Everquest: The first massively multiplayer online RPG, this is the granddad of titles such as World of Warcraft and spawned one of the most amazingly efficient business models the gamig world has ever seen.
Alone in the Dark: Some may attribute Resident Evil, or even Silent Hill with creating the survival horror genre we know today, but this series was the original creeper and was a major influence on both RE and SH and kicked into motion a massively popular genre that is still alive and kicking today.
Wii Sports: Another title that I do not care for myself, this is also one that has had undeniable impact on the industry and it became a phenomenon the likes of which hadn't been seen in almost decades and it managed to pull in people who had never once considered trying a video game before in their life. A mastodon achievement.
Halo: Not nearly the same as Half-Life or Doom in sheer genre influence but the renaissance of console shooters and a key franchise for popularizing the new densely populated online multiplayer competitive shooter scene.
Goldeneye 64: Started what Halo perfected and introduced several revolutionary mechanics (such as free aiming while moving, dual-wielding almost any weapon and introducing new game modes such as one hit kill rounds).
Grand Theft Auto 3: No need for in-depth explanations of any kind here; this was the start of the Rockstar adventure and the trendsetter and beginning for what has become a phenomenon globally, not only the revolutionary gameplay but also in narrative, characters and sheer breadth of concept.
Starcraft: Quick, name a RTS game that has been more influental than Starcraft. That's right, you can't, not even Dune or Command & Conquer comes close and even Blizzard's first flirt with the genre in Warcraft I and II falls short.
Tomb Raider: It had guns, sure, but it wasn't primarily a shooter, it introduced deep exploration as the main objetive in vast 3D environments and has influenced countless games in anything from controls, climbing and scaling mechanics and to puzzle solving in 3D.
There are certainly more but this is off the top of my head and I've only slept three hours...
