TIE Fighter Collector's CD-ROM
This was the first good game I ever played, and still the best game I have ever played. Everything else I played was shit before... Amiga games at my friend's house, weird educational games I had for the Acorn, and maybe a bit of Sonic 2 on my brother's Mega Drive, but then my family decided to buy a PC, and because I was getting into Star Wars at the time, bought me a Star Wars game collection and this was included. It bundled in all the expansions, increased the resolution, and added voice overs to everything. I couldn't believe it - it was like being in my own Star Wars movie, but also being able to be the bad guy, and not even feel like a psychopath. The reasons were just so damn honorable. You're trying to bring peace and stability to the galaxy but those fucking Rebels keep getting in the way.
The Elder Scrolls III: Morrowind GOTY
My first RPG, so I loved being able to choose the skills I wanted to focus on, and ignoring everything else, and the game would let me do it. I loved how there was something new around literally every corner. The landscape felt massive, although now there's been so many open world games since, when I load it up it feels refreshingly small and familiar. The music was atmospheric and fit the game to the bone. The main story wasn't amazing, but it stands as the best the series has had to date. Purists would say Daggerfall had better systems, but I think they were better executed here, and it had none of the horrible dumbing down that followed in Oblivion and Skyrim. Yes, it is possible to rise to become master of all trades, but I believe that is what Codexers call 'fun' and goes against the Sawyerist tendencies of some modern RPGs I could mention.
Jedi Knight: Dark Forces II
Other people have said it better than me here on the Codex, you just need to search for Jedi Knight and you can find so many articulate posts about why this is one of the best shooters of all time. The level design IS that good. Once you get a lightsaber things become a bit easier, although not always - AT-STs can fuck you up easily enough, and the saber battles can't just be swung through (unlike the sequels, where you can just break through saber locks if you click enough times). The story was original (unlike KOTOR), the FMVs were memorable, and the multiplayer scene was just amazing in its day. I think it was one of the most played games on the internet, and for me it got me into multiplayer gaming. The MSN Gaming Zone was the place to be, and I played this to death, whether exploring new maps like Caesar's Palace, or playing excellent mods like Saber Battle X and Ninja Kage.
The Witcher 3
CD Projekt Red said it would be possible to create an open-world RPG with a great story and they absolutely delivered on that promise. Great C&Cs, mature storytelling, memorable characters, great soundtrack, gorgeous worldbuilding, worthwhile expansions. The combat and the levelling systems are the weak points but not enough to drag the story and quests down, which The Witcher 3 does better than any other RPG I can think of.
Fallout New Vegas
It is quite amazing what Obsidian managed to pull off right under Bethesda's nose. Play New Vegas, then play Fallout 3 and Fallout 4, and you'll know what I mean. This is an Obsidian game through and through, reactivity, C&Cs, quirky characters (without being BioWhores), moral questions, and the best implementation of RPG systems I've seen on a first person shooter.
Star Wars: Knights of the Old Republic 2
Everyone correctly understands this is where Chris Avellone deconstructs the Star Wars setting but I don't think enough credit is given to just how fucking amazing the writing is (except for here on the Codex of course). Play KOTOR2, listen to Kreia, listen to the companions and the council, then go and play a BioWare game and you'll see the difference. It says a lot about the industry that the only people still writing RPGs this well is Obsidian. BioWare emphasise the cinematics and the action, and Bethesda don't even try. Obsidian put the heart and the brain into it and KOTOR2 is the finest example. MCA isn't the only one who gets credit for this. A team of immensely talented writers worked on this game and most (maybe all) of them have since left Obsidian, which is a great pity. If anybody asks me what my favourite Star Wars moment is, I'll tell them it is the scene at the Enclave where Kreia reveals all.... and it is even better with TSLRCM.
Half-Life 2 & Episodes
To me, Half-Life 2 demonstrated it was possible to make a first person shooter with likeable characters and a good story without there really being much dialogue. After all, Half-Life 2 is really about the shooting, and there's a lot of it. But there are also varied environments, lots of break up of the gameplay with some light puzzles, driving sections, and exploration, and the design was pretty damn cool - the main visual designer would later take his work to Dishonored.
Episodes expanded the story, made us care about characters like Alyx, and then ended on the most cruel of cliffhangers. Now it seems Valve are happy to make multiplayer games like Dota and Team Fortress 2 and don't give a shit about Half-Life 2 any more, but we are owed an Episode 3 and a fitting end to the story.
Grand Theft Auto: Vice City
This GTA had the best theme (80s neon beach paradise), the best soundtrack and really just the best reason for existing out of any of the GTAs. GTA 3 set the fundamentals but was really just a dour game about the Mafia with a voiceless protagonist who doesn't give a fuck about anything, so we don't give a fuck about him. The main character in Vice City is a psychopath but at least we hear him now, and he's pretty damn hilarious. And I know that if you're like me, every time you think of Vice City you're thinking the same thing as me - just driving down a road, with your favourite 80s song on the radio, watching the city go past. Vice City is a game where you have fun just driving to places.
The Last of Us
The best story I've seen told in a video game, the most likeable characters, with a believable relationship, and stunning visuals (especially in the PS4 edition). The setting is not that original if you've seen The Road, 28 Days Later, and other post-apoc films, but it hasn't been done this well in a game and none of it ever feels tacky. The zombies aren't fodder and there's very real consequences to the outbreak which you see all the time. It stays great right to the end. Some of my favourite moments are towards the end of the game when the other character gets to make their mark a little, and the gameplay becomes much more interesting as a result.
Assassin's Creed IV: Black Flag (incl. Freedom Cry)
This one is optional and subject to change, but I didn't want to put another RPG on the list.
It really is great to go rollicking around the seas on your own ship, finding treasure, blasting away other ships, raiding convoys, attacking forts and exploring tropical islands. I liked the main story too, I thought it had plenty of variety unlike some other entries in the series, and Freedom Cry was a great expansion because of the completely different protagonist and story tone. The AC series hasn't been this fun since... I thought Unity and Syndicate were incredibly dour. Rogue was good, though, which was basically AC 4.5. It is worth picking that up if you liked AC 4.
There's dozens more games that I love but those probably rank as the 10 I think are the best in each of their genres. Half-Life 2 and Assassin's Creed IV may stay or leave depending on whether I remember better, older games, or new games come up in the next few years that are better.