Well, I've been a lifelong gamer, so this is actually really hard to answer. There are so many fantastic games to choose from.
If I'm going for classics, games that redefined genres and forged the future of games, I have to say Super Metroid or Chrono Trigger. Both fabulous, both masterpieces. I loved them both, and Super Metroid made up a large chunk of my gaming childhood.
For pure nostalgia, I'm going with KOTOR or Ocarina of Time. So many hours sunk into both of those games.
Now, I'm a big believer in the idea that games continuously improve with the years. There will always be classics, games that blazed the trail and set in stone the path for the future, but they simply fall behind over the years in terms of technical achievement, production values, and the ever expanding role video games play in the world of art. If I take all of that into consideration, I have to say The Last of Us. It's a true masterclass, a tour de force of narrative and emotional depth. Never has a video game told such a gripping, unflinchingly human tale. And the gameplay, graphics, and artistry are nothing to scoff at either. It's fantastic game in every sense of the word. No game has ever made me feel the way The Last of Us did. I had fun playing it, but there was an ever-present gnawing in my stomach, an uncomfortable nagging reminding me of the heavy emotional toll the game takes on its players. At some points, my hands literally trembled. And at the end, I was speechless, something never happens to me after I beat a game.