I had to think really hard about this question, and although it was hard, the best I could do was to pick 4 games that were the absolute most memorable to me and were constantly fun no matter how many times I played them.
1. SOMA
SOMA is a game I only played once all the way through but I might eventually go back and replay it. This game tells one of the single greatest science fiction stories I have ever seen in my entire life.
I love reading, and I have read many fantastic Science Fiction novels. One of the greatest science fiction novels I have ever read in my life is a novel titled, "Do Androids Dream of Electric Sheep", by Phillip K. Dick, some people may know this story better from it's famous movie counterpart, "Blade Runner". I bring this book up because the amazingly well told story of SOMA is a complete re-imagining of this fantastic novel. SOMA is a an emotional roller coaster of a story that will entertain you, frighten you, bring you to tears, and will make you question your existence and what it means to truly be "alive".
The characters in this game are incredibly deep and complex and you grow to care about all of them. The overall premise of the game is a fantastically well told Tragedy. This game made me cry hard. I can't think of a single game that has ever made me cry so hard, except for SOMA.
I encourage anyone and everyone to play SOMA. It completely changed a lot of personal philosophical views I have on what it means to be alive. The game itself is well put together, fun to play, has beautiful and immersive graphics, and is suspenseful and frequently terrifying to play (it is a horror game). I easily consider it to be one of the single greatest games ever made.
2. Elder Scrolls 4: Oblivion
Elder Scrolls 4: Oblivion was the first Elder Scrolls game I had ever played and I have probably more memories playing this single game than most other games I have enjoyed heavily throughout the years. It was one of the first games I had bought when I got a Play Station 3 and I have probably replayed this game with new characters more than any other game I have ever owned.
Cyrodill is a beautiful, vibrant, and colorful land to play in that just feels humongous with many places to discover, explore, and do whatever you want in. The main plot of the game is a pretty interesting story and although it's not the best story ever told, it's still entertaining and fun to follow along with. The whole game is a deep sand box where you can choose how you want to play with a hand full of different factions that all have pretty fascinating stories. The game is easy to immerse yourself into and it's even fun to sometimes do some role playing in, which is something I frequently have done while playing this game.
I have many good and bad memories of playing this game as well as I have some great memories of doing some outrageous stunts and kills while playing Oblivion. I've built characters in this game that I enjoyed playing so much that I even wrote fan fiction about them based on their adventures in this game.
I can definitely say this game has a special place in my memories and even now I still consider it an amazing game worth playing, last time I played Oblivion was about half a year ago and it's still just as fun as the first day I ever played it.
3. Final Fantasy Tactics Advanced
Final Fantasy Tactics Advanced is another game that I have spent years of my life playing. I played this game obsessively on the Game Boy Advanced as well as I have replayed the entire game twice on two different smart phones using an Emulator.
This game is so amazingly well put together in so many different ways it frequently blows my mind every time I play it. The battling mechanics are very well done, every single action in the game is affected by a large range of different factors. The units being affected by the action, the terrain where the action is occurring, the various stats and bonuses of the character you are using, the level of the characters, the particular job class of each character, the items any individual character may have equipped.
It's altogether a well thought out battle tactics game with multiple different races, a large variety of classes, a huge diverse collection of weapons and armor of various different rarities.
It's very fun to run your clan, do various types of quests and battles, and just trying to be completion in this game is very time consuming and incredibly fun and addictive.
The characters are relatively well written and the story has quite a few interesting plot twists in it that will in fact surprise any new player. I heavily recommend this game, and encourage people to try playing it on their phone, it's a great time waster that is easy to step in and out of, if this game were updated as a phone game, I really think it would be incredibly successful.
4. Final Fantasy 12
Final Fantasy 12 has all of the complex game play and tactics that can be found in Final Fantasy Tactics, but re-imagined in a beautiful and large environment with live action real time combat. The large variety of magic, weapons, armor, and techniques that can be discovered throughout the game compliments the exclusion of actual classes within the game. There are only 6 playable characters, but all of them are extremely important as major characters within the story line, all of them can learn all of the magic, techniques, armor and weapons within the game with complete customization, and you can freely build any of the characters to fit any specific battle style of your choice.
You can personally program all 6 of the playable characters AI to operate in specific ways to properly react to any kind of situation while in combat. Plus you can freely control any number of the 6 characters while in combat or choose to run all of them on the AI that you set in the game. All of this plus the surprising intelligence of the AI of these characters.
It all comes down to the deep and smooth customization of everything within this game you can have as much or as little control of everything within the combat of the game, that makes this game so amazing to play.
Tons of side quests, Rare monsters to hunt, Powerful items and weapons to seek, complex boss fights, amazing summoned creatures that also have pretty impressive AI. All of this packed into a single game!
Plus, one of the most complex and well told Final Fantasy Stories I have ever seen filled with conspiracies, betrayal, mystery, and many twists and turns. All six of the characters have extremely important roles to play in the story and all of them are incredibly fascinating with deep histories and unique personalities.
The world that this game takes place in is absolutely beautiful, and despite that it is designed in a dungeon delving sectioned map style, all of the maps pieced together make the entire world of the game humongous and there are many optional maps that are not on route of most of your destinations but they hide lots of secrets and/or side quests.
Final Fantasy 12 is just one of the single greatest Final Fantasy games I have ever played, and since I last played it for the third time back 2014, I still think it holds up as a great game even to today's standards.
I would say all four of those games are tied in my head as the greatest games I have ever played in my life, and all of them are fantastic in my mind for completely different reasons.