My list is pretty short because I'm primarily a console gamer, but to make up for it I'll only add games that are exclusive to computers.
1: Clive Barker's Undying. This was one of my favourite PC games not because of great mechanics but a fantastic story which threw you right into the thick of the horror. It wasn't entirely scary, but it did keep me invested because it gave little time for you to pause, and the world was quite open so you can stray from the beaten path to have a look around this small estate on Ireland.
2: The Sam & Max Series. Originally on MS-DOS, the games were later remade with updated visuals, sounds and extended stories. This point and click series was possibly the most popular when it first debuted, and even now it remains one of the best point and click detective games around, not to mention the funniest I've ever played next to Broken Sword.
3: The PC-exclusive Unreal games. This is the shooter that turns boys into men with unrelenting arena action like no other game presents. Sure it's not that original when compared to Quake but it has all the fun of that IP and more. The games were split into two 'types', one being an open world shooter that was more story oriented, and the Unreal Tournament games which were heavily deathmatch based. Many often confuse the Unreal singleplayer games for the Tournament ones, even though they're set in the same universe and share one of two words of the name.
4: StarCraft 2. Quite easily one of the better RTS games I've played next to LOTR: Battle for Middle Earth 2 and from the same developers of SC, WarCraft. Not only does it have a great community that vies for supremacy and each player is proud of their army of choice, it also has a fantastic story and setting that is still on-going. If I had to give any reason why Blizzard Entertainment were a good developer, I'd only have to point the person who asked to StarCraft.
5: World of Warcraft. Easily the largest MMO in the US and EU regions of the gaming world, WoW has had huge demand in the past and a steady decline in recent years. Its numbers, while huge, are not a testiment to the game's quality as it's heavily outdated and fails to keep up time and time again. Still a brilliant MMO and the one I'd recommend over most, WoW is a living relic and shows us the best and worst of the MMORPG throughout the ages.