Super Mario Bros.(NES - 1985 - 11 games, platformers only)
Hailed as the best-selling game of all time and the savior of the video game industry. It also made Nintendo a worldwide phenomenon. Run left to right, jump on crap and search for secret levels. So simple yet entirely inescapable.
Why it soared
Though there were scrolling games before it, this is one that everyone played. It wasn't just about getting to the end or racking up an impressive score, it was about exploration and doing things differently from everyone else. Sure you could run straight through, but you'd miss the vines leading to bonus coins, the pipe warp zones to higher levels, the bouncing star that makes Mario invincible... the amount of freedom in one game was astounding. You'd visit a friend to show him something you found while playing, only to realize he found something completely different on the same level. It was a bonding experience when most games were still about competition. Level variations (castle, nighttime, underwater) and legendary music (you know how it goes) also helped make this not just the most important Mario game, but one of the keystone titles for the entire business.
What it did for the franchise
In essence, it allowed Nintendo to live. Bowser, Peach, coins, pipes, it all started right here. Even the sound effects are still used in the modern games and mainstream media alike. Every single screenshot of this game is a piece of videogame history, studied and analyzed to infinity. Flash forward to Super Mario 64 and you'll see the plumber do the same thing all over again, this time for the third dimension. Mario's popularity propelled him into worldwide stardom with cartoons, countless odds and ends and, of course, multiple spinoff franchises. Mario Party is in its tenth incarnation, Mario Kart has seven versions available and the RPG titles are already in their sixth run. Even the original three games have multiple remakes that have additional features. There are so many damn Mario games we had to limit our counting to platformers only. Do you want to count 'em all?
Who it inspired
Everyone. The vast majority of the 700-plus NES games tried to copy the platforming success achieved in the very first Mario game. Major competition wouldn't appear until Sonic arrived in 1991, and even then the hedgehog only managed a temporary victory. After Super Mario 64, it started all over again, with every developer on the planet trying to bottle one ounce of Nintendo's ocean-deep platformer. To this day a new Mario game is expected to rise above all others, and that's traditionally been the case.