We did something similar before but...
Pre-College:
Super Mario World (SNES)
Harvest Moon 64 (N64)
Conkers Bad Fur Day (N64)
Grand Theft Auto 3 (Ps2, Xbox)
Star Wars: Knights of the Old Republic (Xbox)
Post-College:
The Last of Us
Mass Effect 2
Mirror’s Edge
Bioshock Infinite
God of War (2018)... but Red Dead Redemption 2 might pass it up (currently playing it)
Also, I didn't include more than 1 game from a series (ala GTA V). Nor did I include Stardew Valley for similar reasons.
I really like this category, but I'm going to break mine apart more, since I went through "phases" so to say throughout my life. I'm also going to limit myself to one game per franchise.
Lists of games are in no particular order.
Childhood/Elementary School years:
Super Mario 3 - 1st game I ever played
Banjo-Kazooie - 1st game I ever 100% completed, and all time favorite
Desert Falcon - Atari game my dad and I played a lot, competing for the highest score
Pokemon Red - Mowed lawns for most of a summer so I could buy a GBC and this game, along with a CD player. One of my proudest accomplishments as a kid, as I was not good with saving money. Also, this purchase furthered my love for both games and music.
Donkey Kong Country 2 - We didn't own an SNES, but we'd rent one occasionally before N64 came out. I would rent this EVERY time.
Pre-teen/Teen Years (JR High/High school):
Diablo - played this at a friends house (parents wouldn't allow it) and it blew my young mind
Final Fantasy VI - Again, we didn't own an SNES. A buddy in junior high introduced me to the world of emulation, and I fell HARD for this game. Right up there with Banjo-Kazooie for all time favs. IX is a close second, as a bought an entire console just to play that one.
DDR (particulary 8th Mix Extreme and StepMania) - large portions of my money during high school went to the 8th mix machine we had at the bowling alley. Hardest song beaten on the mat: Max 300 on Expert.
GTA: San Andreas - I played the others a lot too, but this one I put the most time and effort into, and completed 100% (Fuck Zero's helicopter mission)
College/Early Post College Years:
Halo 3 - I technically started playing this one my senior year of high school, but the majority of the time spent was in college. The game that brough my wife and I together.
Modern Warfare 2 - I'd like to include MW 1-3 and BLOPS here, as my college buddies and I played these throughout the years. The pinnacle of my multiplayer time. This era comes with a few regrets as well, as we were toxic at times, but I fortunately came to my senses eventually and stopped being such an asshole online (and in general, I guess).
Braid - The game that truly got me to appreciate that games are art. Had to get my jaw surgically re-attached after it fell to the floor after the ending.
Borderlands 2 - Still a favorite I go back to from time to time. One of my favorite villains. Fun gameplay. A rare occasion where I can play by myself, or with people, and have the same level of fun.
Bioshock - Another game changer in general. Shifted my perspective on FPS games. Brilliant story telling, with lots of action and horror. There are much better descriptions on why this game is so great than what I can provide.
Post College/Adult/"The Dad" years:
The Binding of Isaac - A little late to the party here, as I've only been playing a few years, but I have 900 hours and counting. The game I've played more than any other, and I still play almost daily. I'm going to get all those Steam achievements someday.
Celeste: I've talked about this one a lot, so I'll keep it brief. Hearfelt and charming, beautiful music, tight platforming controls, challenging yet positive about the experience.
Hollow Knight - Similar reasons as to why I love Celeste, except for the story. This one is quite the opposite, dark and haunting. The thing that really sticks out about this one is that it's up to you to discover the full story. One of the rare games that deservedly gets the Dark Souls comparisons.
Titanfall 2 - Best shooter of the decade, and tragically underappreciated. Some of the most created levels found in a single player campaign, and fun, frantic multiplayer. Plus, you get to use mechs, what more do you need?
Red Dead Redemption 2 - I had my issues with this game, but I feel the world building elevates the experience above any problems. Again, a lots been said about this one, and NakeyJakey's video on the game sums up my problems pretty well. But the characters, the story, and the things I experienced in the world, left a profound mark on me.