Great topic idea, I'll get back to it when I have time to write out a lengthy post.

My top 3 hasn't changed in 20 years, all 3 have an emotional attachment

1. Everquest. I played it from the end of '99 to 2005. I started the game when I was at my lowest as a get away from the world. While playing I fell in love with a girl 6,000km away. It lead to me immigrating to Canada in 2002 and get married. Happily ever after. Besides from completely changing my life for the better, it was/is an amazing game as well, extremely hard and unforgiving, but so rewarding with a well oiled group of people.

2. Civilization (1991). I was into board games at the time, getting bullied at school, not a fun time. Then a friend from school brought a copy of civilization over and we played it all night into the morning. It was a new genre to me, so many possibilities, open ended, so many ways to play. I played it it for years, altered the game by hex editing the exe file, then bought all the follow up versions. I did finally get enough it, but so many memories and different friends I've played it with.

3. ICO (2001). Apart from being a great game, I started playing it together with the girl I met on Everquest when she came over to visit. She had to go back of course and we left the game halfway. After I emigrated I bought the game again (NTSC version) and we finished it together (while also now playing Everquest side by side)

I doubt anything can ever penetrate my top 3.

Runner's up: Valkyria Chronicles and Dark Souls. Both great games, yet at the time our youngest had severe acid reflux and could not sleep in his own bed. He could only sleep while on my on my wife's lap, holding his head up. Thus we had shifts at night and he would be sleeping on my lap while I was playing those games. I hope I dind't screw him up with Dark Souls lol. Even though it was a bad situation, it was also the most peaceful experience with my son sleeping on my lap. Best recipe for gamer rage! It's probably why I don't have the patience anymore for Souls games, he grew up (healthy :))

Gotta say, I highly approve of all 5 games you mentioned.  Some of them actually are in my top 50 games of all time, and the others would probably at least make my top 200.

1. Everquest - Mostly, I just played MMOs for several years during the late 20th/early 21st century.  I spent several months with Everquest, but Final Fantasy 11 is what hooked me for about 2-3 years.  Obviously, Everquest is the game that changed your life.  Congrats on finding the right girl.

2. Civilization - Even though my favorite to play is Civ. Revolution, I probably have more fond memories of the first Civ game.  There is that epic moment when I think I'm doing great, I already conquered another civilization, and I'm exploring with my Catapult, when tanks suddenly appear out of the darkness.  "Oh shit!" 

Civ 1 was the game that got me into PC gaming.  I remember my friend playing it and some other friends were watching him and one said, "You just researched Gunpowder, but you don't know Horseback Riding yet."  That statement alone intrigued me, but I didn't have my own PC yet.  A couple years later I went to college and got my own PC.  Civ 1 still seemed like the most popular game, because I was playing it and several other guys I knew were too.  They told me that the AI players would not use nukes on me unless I used them first, but I found that was not true the hard way.  I think I broke so many peace treaties that the AI just decided to nuke me anyway, lol.  

3. ICO - Definitely a great game and a great couples game.  My wife and I played it together.  That whole handholding mechanic makes it feel like it's just two people against the whole world.

4. Valkyria Chronicles - I think both 1 and 4 are great, but I prefer 1 for the story and characters.  The first one also just felt awesome in that I really thought the developers were trying something bold and new with making this game.

5. Dark Souls - For the past decade or so my most anticipated releases have been the Dark Souls games.  The first one is my favorite though.

You have great taste in games, and it sounds like you made a lot of great memories along the way.

Yoshi's Island
This is super fun. Amazing level design, tight controls, great graphics, memorable music, loads of stuff to collect. It's just an absolute pleasure to play through (and I do so regularly).

Tomb Raider II
I'm a big fan of the original TR series. I love the controls, the grid based design system, and how methodical everything is. The sense of scale is also incredible. TRII gets the edge over the original as I tend to prefer the level environments in this one, and everything is a little more polished. It's also interesting to challenge yourself when you replay it (eg all kills, no medipacks, pistols only etc)

Super Mario Bros 3
The SNES version is what I grew up with, so that's what I think of when this game is mentioned. This evokes wonderful childhood memories, as it's one of the first games I remember experiencing. It's not coasting on nostalgia though, as it's simply a fantastic game (and I love it for many of the same reasons as Yoshi's Island).

Super Mario Bros 3 is one of the most amazing games I've ever played.  I think the thing that especially amazed me was just how many secrets they seemed to cram into it.  This was the pre-internet era, so I would just keep replaying many of the stages over and over again just to see what secrets I could find.  The most amazing thing to me was the Hammer Bros suit, because it's this powerful suit that you have be a good ways into the game just to find it.  There are a ton more secrets that they buried everywhere.  It's like digging for gold in a field full of treasure.

Thanks. Civilization was amazing at the time, instantly hooked. I also found out the hard way about nukes and global warming due to nuclear fallout. Gandhi of all people nuked me! Ans always hilarious to beat a bomber or battleship with a phalanx unit haha.

Zelda. Just exploring, battling, and finding stuff is so much fun. I guess part of it is nostalgia since I’ve been with the series since it first released in the US. But they keep building on that, particularly with A Link to the Past, Ocarina of Time, Twilight Princess, and Breath of the Wild.

Final Fantasy VII. The dystopic yet colorful setting, the story, and the characters all do it for me. They threw everything but the kitchen sink in. I usually play it once a year.

Dragon Quest.XI. The polar opposite of Final Fantasy. Old school RPG goodness with a modern aesthetic.

1) Homeworld
This game offers one of the best sci-fi stories which is a struggle of a race trying to find their way home. Its emotional and the gameplay plays it out perfectly. Homeworld's gameplay is one of the first 3D RTS games where you have full 360 control of the camera and the freedom on the map. This IP could easily be a movie/series. Its a violent galaxy in the Homeworld universe, one i couldn't recommend enough.

2) Half-Life
Saw an advertise on an old video show (Cannot remember the name) seeing for the first time a player interacting with an NPC. Having them follow you and help you was quite incredible at the time. Half-Lifes story is what makes it great, a mystery experiment gone wrong. I am sure not many need to know how good Half-Life is.

3) Halo 3 / Perfect Dark
This is a toss up, i just couldn't pick which one is my third favorite. Halo 3 has an incredible story with one of gamings most iconic character. The struggle between the human race and the highly advance covenant. It plays so good on the 360 and looked absolutely amazing for the time. Loved the relationship building, the fight and survival. Perfect Dark was a game that had so much hype behind it, and to live up to the spiritual successor in Golden Eye. Joanna Dark was just a fun and interesting character, being the perfect female James Bond. The things you do in this game and the things you can do was just top notch, even to today's standards, PD does things better than most modern day FPS games.

The basic gist of my top 3 is if all games were suddenly deleted and I could only play that one game for the rest of my life, I would still have fun.

Okay here goes.

#3 Mario Kart 8

Alright, it's a Mario Kart game. Everybody loves Mario Kart, right? Nothing special, nothing outstanding. But wait, there's more. This is the best fun racer of all time! This is probably the best party game ever. This has got to be that one game that nobody on the entire planet can ever possibly loathe and that everyone loves, and you know why? Because it's magical! This, my friends, is perfection in every possible way. The track designs, the fun, the graphics, the item selection (yes, including the Blue Shell of Doom and Destruction!), the music, oh my god the music, the online experience, the multiplayer, the velocity, the balance, the sheer chaos, the nostalgia... Mario Kart 8 is finger-licking good. I got this with my Wii U and loved it ever since. No matter if I pay it alone or with my gf or with friends on my couch or even with random strangers online - this game never gets old. Never! There is a reason why this is the best selling game of the Wii U and why MK8D is on the way to become the best entry in the entire franchise. Actually, no... there are a ton of reasons!

#2 The Legend of Zelda: Breath of the Wild

Now everyone and their mum knows this game, there's no need for me to explian why it's good. But what Botw gave me was an emotion that I have not felt in a looooooooooooong time, and that is the feeling of complete and unconditional investment. When I played Botw I was truly in Hyrule, in this game world, in these beautiful environments, and it truly felt like I did all these things like crafting and fighting and exploring and surviving myself. I went all out of my way to explore the land because I was genuinely curious to see what I can find and what awaits me behind the next hill, up the next tree, across the next river, inside the next chest, beyond the next valley. I was hooked right from the start and I loved every minute of it! I really don't know why and it is somehow saddening that I can't get this feeling anymore but I remember that I used to have this feeling much more often when I was a kid. Nowadays I just play a game and that's it. No deep attachment. It just passes my attention. But not ths time, this is different. Botw is a special game because it reminded me of why I love video games in the first place. 

#1 Super Metroid

Super Metroid is my favorite game of all time and I highly doubt that any other game will ever touch it, past, present or future. I love the story, I love the ambience, the atmosphere, the lore, the weapons, the surroundings, the enemies, ... everything just fits so perfectly, it is absolutely amazing.

How I wish I could relive those moments when I played it for the first time! I remember that it came with a big guide book that contained oh so much info, images, maps, details. I was genuinely intimidated when I played it, I couldn't stand the intensity! Everytime I entered a new room I had to press Start to check the map. Not even a single step done, just check the map and compare it with the guide book. The insane atmosphere was unmatched, and it grabbed me by the balls and never let go! This investment is exactly what I meant when I talked about Botw before.

I love how you start off with almost nothing and can be owned by the most basic enemies, but then you progress, you become stronger and stronger until one point where the power balance tips so much to your favor that you can just fly through entire rooms filled to the brim with dangerously armed enemies like a knife through warm butter. And I love how every new weapon or item you get is useful and meaningful. I love how the game forces you to think outside the box when you are stuck. I love the feeling of excitement when you reach an unknown area and the thrilling expectation of what's next to come. I love the bosses and their battles. Some of them even tell a small story when you pay attention. My god, Kraid with his giant ass body was so insanely intimidating that I wished I could head back out of his boss room and catch a breath first, but fuck no, once you're in his chamber there's no way out until one of you goes down for good. Also, his cries of pain will always ring in my ear. I love all the secrets and hidden areas that you wil find on your route. I love that each area is completely distinct from one another and feels unique. I love the quite and unsettling moments here and there, followed by action packed battles with space pirates and indigenuous beasts... I could go on, but I think I've made my point.