Here's some picks that don't make me want to curl up in the fetal position and rock back and forth. Though I'm probably forgetting a lot.
1. Tie: Super Mario Bros.- It's the first modern video game. It invented much of the basic formal language of the medium that we recognize today, and the methods by which developers relate that language to the player. Not to mention that it single-handedly saved the video game industry from oblivion, legitimized the console market, and was the best-selling game of all time by a large margin for over two decades (fuck you, Wii Sports). Pretty much every game since in a large number of genres can trace some of its roots back to Super Mario Bros. Well, that and/or...
1. Tie: The Legend of Zelda- If Mario revolutionized the "how" of gaming, Zelda revolutionized the "why." It wasn't the first game where the main object was to complete a story as opposed to getting the high score, but it was the first to do so with an appropriate sense of scale. It was an epic adventure. It looked like it, it sounded like it, and most importantly, it played like it. To perhaps an even greater extent than Mario did, this was a game that completely redefined the notion of what a video game could do. Any game that claims to engross the player in an expansive world full of secrets to discover owes something to Zelda. Hell, most games that try to tell any kind of story owe something to Zelda.
2. Super Mario 64- Nobody knew how to make a game work in a three-dimensional space until Super Mario 64 showed them how. Ever manipulated the camera to see where you were going? Ever intuitively landed a jump or some other maneuver in a 3-D space? Ever used a fucking analog stick? You have Super Mario 64 to thank. Not to mention that the game shook up traditional notions of progression structure and level design and was the first game to perfect fluidity of character movement.
3. Pong- You gotta start somewhere. True, it's technically not the first video game ever, but it's certainly the first with any kind of longevity or wide influence. Plus, it took gaming out of the arcade and into the home, birthing the console market. Put simply, there would be no video games without Pong.
4. Tie: Metal Gear Solid and Half-Life- There have basically been two (somewhat opposing) schools of thought in mainstream video game storytelling over the last decade (there's a third, arguably better one that mainstream developers mostly don't utilize, but whatever, that's for another thread), and these two games (released at around the same time...coincidence?) are more or less their founders. In the MGS style, story and gameplay are mostly kept entirely separate from each other, with gameplay switching off the running time with cutscenes that carry most of the weight of conveying the story. In the Half-Life style, the gameplay and the story run parallel to each other, with the player always in control in a story that unfolds at the player's own pace and level of interest in the smaller details. I'll be shocked if you can find me more than one narrative game from a major publisher released in the past ten years that doesn't follow one of these two formats. Like, let's say maybe a game where the gameplay mechanics and the story are actually inherently intertwined with each other. I say "more than one" because...
5. Shadow of the Colossus- ...of this. Oh, how I wish this game could be sitting pretty at #2, The Godfather to Mario and Zelda's Citizen Kane. Unfortunately, the industry hasn't learned nearly as much from this game (and probably Ico, too, for that matter, though I haven't played it yet so I can't make any judgments) as it needs to. Even so, SotC is still the best argument out there for video games as their own legitimate art form, and pretty much the only one on the shortlist to come from a major publisher.
That's all for now, maybe I'll do more if I feel like it. I seem to have incidentally mainly covered importance in the development of games as a storytelling medium above all else for some reason, which leaves out a lot of very important stuff. Oh well.