Well, I think there are multiple potential candidates depending on how you define greatness. I think these few are certainly the most influential:

• Super Mario Bros. Possibly the system it ran on was more important, but this game was a system seller for the system that single-handedly saved not only the entire video game industry, but probably the very concept of video games at a time when it was looking like it'd just be another fad that faded away right along with bellbottoms and pet rocks, with what was left of it remaining caged in Japan. Mario 1 was most people's first platformer, I also have to think that the first damn goomba in 1-1 probably holds the crown for the highest kill count of any entity in the universe.
• Tetris. Infinitely playable and probably infinitely played, and you can get it to run on damn near everything. Everyone knows Tetris, even people who haven't played it or any other video game.
• Doom. Just, Doom. Yes, Quake was more advanced. Yes, Quake was technically the actual technological forefather to the polygonal 3D games we play today, and many game engines still include tiny bits of Quake's original code. But there would be no Quake without Doom. It certainly wasn't the first FPS, but it's the game that cemented the FPS formula for good and firmly established the x86 PC as not only a viable gaming platform, but the king of gaming platforms from that moment until this very day. Ever since Doom, outside of specialized arcade hardware the PC has been the powerhouse platform for the biggest, most technologically demanding games. After Doom game out everyone wanted their own "Doom clone" on their platform just to show that they weren't just another me-too, also-ran.
• Street Fighter 2. The genre defining 1 on 1 fighting game template. Enough said.
• Chrono Trigger. This game showed everyone not what a console RPG was up until that point, but what a console RPG could be if you put actual effort and creativity into it and didn't just crank out another grindy and soulless, swords-and-sorcery-go-kill-the-dragon yawn fest just to keep your franchise going. Its contemporary Final Fantasy games almost got there (especially 6), but Chrono went the full mile. The feats Chrono Trigger pulled off on the humble SNES as well as many of the innovations it brought forward were far ahead of its time and it took literal decades for the genre to catch up to it -- including quite a few entries from its own studio.
• Final Fantasy 7. This game is objectively crap even compared to many of its peers. But there is no doubt that it was the next stepping stone from Chrono Trigger that finally firmly launched the console RPG into mainstream territory, made the genre as a whole truly successful, and was an awful lot of people's first RPG. It probably made a significant and permanent contribution to the formation of weaboo culture, as well.
• Half Life 2. No, not the first Half Life. Not Opposing Force and not Blue Shift, either. There was never before any hype and anticipation for a video game like there was for Half Life 2. In the months leading up to its launch it was all anyone talked about. Not Doom 3, not the new Warcraft. Half Life 2. And of course with Half Life 2 came Steam, and we all know how that turned out. Sure, Steam itself started life as a patch delivery and server browsing platform for Counterstrike, but up until Half Life 2 appeared in it, nobody cared. The impact Half Life 2 had on everything is absolutely undeniable, and that doesn't just include the horde of games that came after it attempting to imitate its unbroken linear first person narrative and setpiece based game design as a cash grab, not to mention that phase in first person shooters where seemingly everything suddenly had to have physics puzzles in it...