Might and Magic VI: The Mandate of Heaven
Back when I was a kid my grandad used to play this game and my cousin and I would watch almost mesmerized by this wonderful game. I recently purchased it from GOG and have set out on my own nostalgia-filled journey across Enroth.
This old jewel comes from a time when there was none of the modern day hand holding. The game drops you right by the gates of a small town and says "Go there and you'll get your first quest, got it? Now fuck off."

The game doesn't have any tutorials or tips so most of it is trial and error: am I strong enough for this dungeon? No...*insta-killed* But I don't feel that this is a problem for the game, it leads to a much more cautious and methodic playstyle where you really take your time to learn about the world and all the enemies that you encounter - their strenghts and weaknesses.
The game puts you in charge of a party of four individuals which allows you to combine and explore many of the games different classes, you're therefore allowed to tailor your own playstyle based on the strenghts and weaknesses of each individual in your party.
The gameplay is very fun and diversive as the game allows for both turn based and real time combat; pressing enter will put you in turn based mode where everyone will freeze, allowing you to carefully choose spells and attacks and then wait for the enemy to respond. This mechanic is one of my favourites in the game, the ability to carefully plan your attacks and think about what you're doing instead of just madly running around buttonmashing spells and meleeattacks.
The game also has a great amount of spells for you to use (if anyone in your party can use them). There are many categories of spells: earth, air, fire, body, mind, sprit etc. all with different spells that all have their different effects. You also have to make sure that your characters have learned the skill required for each category of spells.
As for the non-magic ranged attacks there are bows and crossbows, and for melee there are a huge variety of spears, swords, maces etc. This combined with all the armour, rings, amulets, boots, cloaks etc. makes lootig very interesting and it's very rewarding as you fight your way to the chests in that big dungeon you are too weak for but choose to explore anyway.
As for leveling: the whole concept is based on skills. to use a certain weapon or spell class or wear a certain armour you first have to teach that partymember the required skill. When you level up you get points to put into those skills and when you reach a certain skill-level you can become an expert in that skill, after that you can become master of that skill but master usually requires more than just skillpoints and gold. I love this way of leveling as it gives your character so many options to grow and you get to tailor every character with their skills to suit your way of playing. And when you've come a bit further in the game and your characters have become stronger it's always fun to go back to those monsters that usually took ages to kill but that you now can kill in a matter of seconds.
The graphics are on the other hand very bad, nigh on ugly. But if you can overcome the oldey-timey graphics then there's actually some beauty in the game; mainly in the dungeons. The game features a huge variety of dungeons for you to explore. Every dungeon feels like a new experience and they all feel and look different. There are your standard caves and castles but there's also different temples and huge mazes and even one dungeon which haves you make your way into a great cave in which there's a HUGE pyramid, it truly is one of the best dungeons I've seen in any game. The outdoor environments are also very good and diverse but not amazing: deserts, islands, winterlands etc.
The game also has a great soundtrack which I've mentioned many times, a few of the songs are some of the best I've heard in a game, might be for the nostalgia but still: a great soundtrack!
I could go on and on about how great this game is but I guess I'll stop here. In short: if you like challenging RGPs and don't mind old graphics then buy this game! It's supercheap on GOG and don't require much space so don't hesitate to buy it. I promise you it's worth it!

The Elder Scrolls III: Morrowind
Despite the amazingness of Skyrim neither it nor Oblivion manage to capture me like Morrowind did. The world of Morrowind and its atmosphere is unmatched by the following titles in my opinion and I have to say that I therefore prefer Morrowind. There's just something about this game that captures me like no other. I love to just walk around and explore the world, talk to all the people and listen to the great soundtrack. This game is definitely one of my favourites.

Halo Combat Evolved
I can't help it but I love this game, and the remake was like a gift from the heavens. The first is usually the best and for me the Halo series aren't different. Despite its age and the other games new and improved gameplay this still remains as my favourite. Oh the countless times I drove round and round that island before realizing where I was supposed to go! Fun times.

Far Cry 3
I really liked the firs Far Cry, and it was still fun to play but not as fun after that point (if you've played it you know exactly what I'm talking about). I also really enjoyed the second Far Cry, despite all its problems I still think it's a bloody good game. But nothing beats the third game. Far Cry 3 is without a doubt one of the best FPSs I've ever played. The world is so colorfull and rich and the characters are amazing, this combined with great gunplay and driving mechanics makes this one of my absolute favourites.

Metro 2033
I can't leave this thread without mentioning Metro 2033. This game has one of the heaviest atmospheres in any FPS I've ever played and the feeling of dread as you walk through the metro is unmatched. I love this game despite all its problems and it remains one of my absolute favourites.
As for Metro: Last Light I have no doubt it's a great game. After seeing TBs WTF I am convinced. But sadly I don't have a computer that can handle that beast so I'll have to wait. But I know that I'll love it.

Yeah... I am into rocket science. For those who don't know, KSP is a space program that allows you to build your own rockets to perform your own space missions. But let those green men fool you. This game is very complex and very hard for first timers! But once you get the hang of it you will never want to let it go!

The Homeworld games are a sci-fi themed RTS games that first introduced the concept of fully 3D environments (meaning the game doesn't take place on a "plane" like in Age of Empires). The games have a surprisingly good story and amazing gameplay! Why? Because unlike other RTS games where you are leading an empire to basically rule the world. This game instead takes the path of making the player merely trying to survive a harsh universe. You are leading the last survivors of a once vast empire. So you will never have a big army and you have to strategy a whole lot more because of it. which I think is great! And that's why I love it!

Yes I am a science fiction whore. I just love this game because it was my first horror game. Fuck you if you want more info.

No, I'm not just saying that. This is, by far, my favourite. Before this game, I never - NEVER - made it through to the end of a horror game. They scare the shit out of me (pardon my language)! By about half way through the very first map in this game, my hands were actually shaking too much to play. Normally, that would be when I quit, but the delivery of the story line and my curiosity about the whole game kept me playing (and a large support group of friends, all huddled behind me while my computer screen was projected on a TV). I really just love this game. I've probably played it.... 5 or 6 times now and watched LPs of it too often to count (other people's reactions are quite reassuring that I was not alone in my terror).

Of course, I could say I've never experienced a game with such great atmosphere before, but I don't think MarioKart or SIMS really even count.

Within the first 20 minutes of gameplay, I had become attached to the characters. I love how the characters are portrayed and the variety of narrative devices used to give depth to them. Seriously though, the characters. Having great gameplay and aesthetics were just a lovely bonus.

I'm tempted to say that ATDD and The Last of Us are tied for my favourite. I put this game second only because I haven't quite forgiven Naught Dog for the ending (it was excellent, but emotionally traumatizing).

I think I saw someone mention this game earlier in the thread. I bought it shortly after downloading Steam (so.... early 2013). Even though the character animations make me cringe once in a while (I have to remind myself that this is a relatively old game), the general atmosphere makes it completely worth-while. The whole world feels like it could span out for ages and the game does a really good job of making you feel like it's part of something much larger. I've played both Morrowind and Oblivion, but I definitely prefer Morrowind's set-up.

• MarioKart (GameCube and N64 version)
  
• SIMS (with Unleashed expansion pack)
  
• Zoo Tycoon (with both expansion packs)
  

These were my childhood games. It was hard to convince my parents to let me buy games that *may* be violent, so I didn't have 99% of the nostalgia-inducing games everyone else played (they actually thought Pokemon was violent)

Obviously my parents didn't know about my killing sprees in SIMS (or how babies were made in the game) and, ironically enough, the first game I ever owned was:
http://gamingcheats.com/materials/images/games/2655.jpg
or
http://www.searchamateur.com/pictures/deer-hunter-2004-4.jpg
or
http://image.allmusic.com/00/agg/cov200/drg000/g079/g0793758gux.jpg
One of those three, it's been at least 8 years since I've even interacted with this game.

I'm not sure why or how I managed to land my hands on this game (actually, it was an Easter present from my dad), but I thoroughly enjoyed killing Bambi's mother (which actually results in a game-over because you're not supposed to shoot the doe). I know. I'm terrible.

On that topic, I'm kind of curious what everyone else's 'first game' was.

Not sure if that is the actual game but I remember having one of them for PC back in what must have been 97-98 when I was but a small laddie. I only remember bits and pieces from the game but I do remeber that it was fun ^^
The first game for more experienced and older gamers (i.e. not children) was Ages of Empires II when I was six. My grandparents thought that every game was a kids game and this game had knights in it: perfect gift for a kid. If only they had known how brutal this game was (at the time) as bodies covered in blood decomposed on the ground as armies marched over them.

The Walking Dead (Season One)

This is the one game I cannot bear to restart playing. It is probably the first game to make me drop down onto the floor and start weeping. Well done characters, great art style, and possibly the most realistic child character I have seen in a game. Can't believe that one of the writers would go on and write After Earth :/

Crusader Kings II

ALL HAIL THE GREAT EMPEROR JANUS HUDSON OF BRITANNIA!

Amnesia: The Dark Descent

This was a game that was impossible to exclude from this list. While other games call itself horror, they never scared me and as a result I stopped playing horror. Friends poked me to try this game saying "No really, it's a really scary game" and while I took that with a massive dose of salt, I realized that they were right. I didn't sleep for a while.

Dynasty Warriors 5

In this game you can play as a 3rd century flamboyant army officer who dispatches his enemies using claws. This game is awesomeness on a plate.

Harry Potter and the Prisoner of Azkaban

Potter fans should pick up this game for the PS2, IT HAS OPEN WORLD EXPLORATION OF HOGWARDS FOR CHRIST SAKE....AND YOU CAN RIDE THE HIPPOGRYPH

Spec Ops: The Line

I hated myself after finishing this game. I felt....well.....damn. This game is depressing on a whole new level, telling you that you are a horrible person for almost every second and basically criticisms the conventions of a video game IN a video game.

Spyro: Year of the Dragon

My PS1 childhood was wasted on this game, and I am glad of it. It's broken in some areas (like the skateboard minigame), but that is nothing compared to the massive grin I was pulling almost every time I started to play this game

Bioshock

A game set under the sea starring Dr Nefarious from Rachet and Clank with big ass robotic monsters? SOLD. The twists and turns of this game and the story is one of the best I have ever played in my life. Shimerman sells the hell out of this game and every element assists the story...now I feel like replaying it.

Grand Theft Auto: Vice City

Best...soundtrack....ever!

Ride to Hell: Retribution

What can I say? It has been game of the year since the very beginning. With it's amazingly well crafted story, excellent voice acting, and the graphical fidelity (Crysis be damned!) And the gameplay helped the story of a veteran being harassed by biker gangs and goes through an emotional turmoil. A true classic for the ages!

Silent Hill 2

I am really surprised that this game has made no appearance on this list, and you are all going to hell for not playing it. Gameplay complimented the character, fantastic atmosphere even to this day, and a story that should still be held in extremely high regard.