You're essentially asking us what our three favorite games are, so don't beat around the bush.
Over the years I've played many games and I've enjoyed some more than others, but still I find it very difficult to place my favorites in a conclusive and arbitrary list. I enjoy them all to different degrees and enjoy them for distinct and varying reasons. For the sake of contributing though I'll pick three I feel like talking about and explain why I enjoy them.
Ico
An experience masquerading as a game, because no other media format could give the player the same experience. Minimalistic in all aspects of it's design and brilliantly crafted. The game's story is as simplistic or rich in lore as you want it to be, leaving many key aspects vague for the player to fill in with their imagination. You play as a boy, with no super powers, cast out of his village for being burdened with a curse. His horns are seen as an omen, a plague for the village so he is cast out and taken to an ancient castle where he is to be sacrificed to the queen like many before him. He finds what appears to be a girl, but is so much more. With the mentality of that rivaling a small child she has been caged her entire life, kept from the outside world. She knows absolutely nothing, yet shines with a radiant light much like an angel.
At first Ico is merely looking for a means to escape and seeing as the castle is infested with stone statues that only move when this girl comes in contact with them, he needs her. The core gameplay is puzzle esque, but you don't play Ico for the gameplay, you play it for the atmosphere. The castle is brilliantly designed, it's architecture reflective of a master craftsman. With the birds chirping over and above, the sounds of water cascading down the distant rocks and the sun's warm embrace beating down on them they wander the ancient halls for freedom.
I won't spoil anymore of the game, I feel like you should just experience it yourself.
Super Metroid
My personal favorite in the series, what is there to say about this game that hasn't been said? Every pore of this game oozes with atmosphere as you play as the badass bounty hunter Samus Aran exploring planet Zebes. At first the planet seems lifeless and abandoned, but soon enough she realizes it is crawling with Space Pirates and her nemesis Mother Brain has been revived. Using the powers of the ancient Chozo you explore and put an end to Mother Brain, Ridley, Kraid and all the other creatures that seek to cause chaos in the universe.
The controls are tight and extremely responsive. The powerups gained constantly allow new areas to be explored often times intertwining inside each other opening up shortcuts. The music is haunting and alien like. The boss design was out of this world awesome, very intimidating. Secrets were exhilarating and rewarding to discover. Plus the devs thought far enough ahead to include techniques such as "shinesparking", "wall jumping" and "mockballing" which adds INSANE depth allowing you to access areas you normally wouldn't and shouldn't be able to yet. Speed runners consider this the BEST speedrunning game ever made and I have to agree with them. One last thing, the level design is unreal in how natural it all feels. There is so much I want to say about this game, but I don't have the time and you probably not the patience. Here is an article outline all the reasons I enjoy the game though if you care.
I've been playing video games for over 18 years and none have surpassed Super Metroid in the amount of care and attention to detail it was given. It is a work of art, plain and simple.
Dark Souls
This game absorbed my gaming life for over a year since it's release. I'm glad I've since satiated my addiction, but I don't regret spending over 2,000+ hrs on this gem. Let's get into this, shall we? It is an action rpg with a unique battle system. You freely control both hands and pending on your equipment, you can block,parry,light attack, heavy attack and so on. You are completely free to customize your armor and both hands with whatever weapon/shield/weapon setup you desire.
The reasons why I enjoy this game are quite difficult for me to explain. Let's start with the music score, absolutely gorgeous. The melodies contained within are either dream shatteringly magical or perfectly capture the energy and raw emotion of battle. The game's lore is one of the deepest I've ever been able to experience in gaming and best of all is completely optional and not forced. In an era where qte sequences and long, drawn out and overplayed cutscenes reign supreme this game completely defies all that and treats the player with respect and grants them the option of ignoring it all together. I don't possess enough character space to do this game's lore justice, but if you want to know why I'm so passionate about it check out this youtuber's videos detailing and outlining the game with pleasant commentary.
It doesn't end there, even the item and equipment placing ties into the game's lore. Just as drowning as the game's story is, so are the game's battle mechanics. I won't even try to explain to anyone that hasn't played but this game is just amazingly refreshing. Shields have block % and stability which is indicative of how much stamina damage you take, different weapons may have normal/magic/fire/lightning damage which is calculated according to the enemies def properties and so on. So much thought and detail has been placed into this game.
I haven't even talked about how the game plays almost like a Metroidvania in how you constantly open up new shortcuts and explore new areas. (which on your first run through the game is quite tense, always worried about what is beyond the corner) Areas are varied and vibrant. Giant castle filled with sentinel guards? check. Pitch black cavernous tomb filled with animated skeletons? check. Ethereal crystal filled cave with invisible bridges and moonlight butterflies? check. The list goes on, even without 1080p this game is beautiful in design.
I could go on, but I'm really hungry and feel like stopping. lol