Doom (1993). Before id Software existed, games that had scrolling screens wouldn't even run on computers due to how slow they were. Not only did they solve that problem, they created the first
3D PC games that performed smoothly, and Doom was a massive jump forward for its time with dynamic lighting, intricate, texture-mapped walls, incredible character models, and innovative level design (verticality in levels, walls at angles other than 90 degrees).
Doom also paved the way for concepts like multiplayer Deathmatch/Co-op, modding, and free-to-play (with the Shareware concept). It's unbelievable to think a single game could do so much for gaming in general.
Not only that, but the theme of being a marine on an isolated military base in outer space that fights demons from Hell made for an incredible atmosphere of isolation and tension.
It's still extremely playable to this day - simple albeit tense gameplay, interesting puzzles, phenomenal sound, immersive level design, and hard-to-find but obtainable secrets in abundance. The game also has an aura of badassery that cannot be denied - the logo itself is incredible.
I'm waiting for a game that challenges what a video game can be like Doom did.
Otber inspiring games:
Mass Effect Series: Not only is the series devoted to its characters and your interactions with them, you literally get to play through the entire series with the same character you've created, and decisions you made in previous games will affect the other games. The sense of immersion this creates in the storyline and universe is immense. The best part is that many of these decisions matter quite a bit, so you'll only get the full ME experience by playing the entire series many times.
Portal 1/2 - I'm going to agree with
@Wyote on this one. Portal not only proved that puzzle games could be huge, rewarding, cerebral affairs, but that they could deliver a cinematic experience that rivals cinema itself. A major revolution of the genre.
Minecraft - While it may seem a cliche choice, not only does Minecraft allow you to basically create any structure you desire with the elements of the world around you, it allows you to create switches. From switches you can create logic gates, and from these you can create...
computers. Minecraft allows you to create functioning computers within the game, just an example of what a simple engine can allow for in a video game. The only issue with the game is that the experience requires your creativity, or at the very least, an agenda.
Will probably post more later...