Oooh, good topic.
Games that defined PC gaming for me:
My first computer was a Vic 20, but since most of the games were cartridges for that, I will skip it. Although I have to say, I programmed a game called "Maze of the Minotaur" that was so big you had to load the second half of the game from the datacassette.. of course with 2.3kb of memory it didn't take much to run out..
About the same time, at school, on the old Apple II's we would play Wolfenstein and Oregon Trail, and I suppose you could say those were the first to wake me up to "PC Gaming".
My second personal computer was an Apple IIc, and on that I recall playing Kings Quest, Zork, Leisure Suit Larry, and Hard Hat Mack, but the one that really defined gaming for me was Ultima 4. I played that game for an entire summer, about 800 hours worth, and when I got to the very end and blew the horn, the game crashed. After that I got hooked on Wasteland, and the Bard's tale games were fun too.
At the same time I got my Apple IIc, my friends got C64's and I loved going over and playing Wizardry and the others in that genre (Zork with some graphics, lol).
Then there was a period where I was in college, and I would have to say the MUDs were what got me. In fact, I got so addicted it cost me the ability to stay in college. Not only did it get me in a lot of trouble (got kicked out of several computer labs and got caught stealing people's accounts so I could log more hours on the VAX), I got to the point where I was playing 20 hours per day and sleeping during classes. My gpa slipped below 3.0 and my dad stopped loaning me money for tuition so I had to drop out. While working to save (and to get off my parent's taxes so I could get a student loan), I knocked up my girlfriend and never went back. Such is life, but you could say that those prequels to MMORPGs really did define my life.
After that I got my first "IBM compatible", a Packard Bell 486sx33 with 2mb of memory. On that I played games like the D&D stuff (Pool of Radiance) to recapture the old Bards Tale type games (and it was cool to play D&D licensed stuff), but what defined gaming for me at this point was Dune 2. That paved the way for all RTS games like Warcraft 2, Command and Conquer, and eventually Red Alert, StarCraft, Age of Empires, etc.
FPS games that defined the genre for me started with Wolfenstein 3D, which was great because I used to play the original Wolfenstein on Apple II's at school. Doom, of course was huge, but I LOVED Duke Nukem. That one got me to dial up with friends and play 1v1 for hours on end. I even played Doom and Duke Nukem over null modem cables at home with my roommate. So much fun... Years later when Call of Duty came out me and my friends go so involved I built a server and ran it for years.. so long in fact that I forgot it was running under a cabinet behind my desk. It was on an old high speed internet connection we only kept for a failover and never used, so this was the only computer on it. One day I logged onto it only to find it had been hacked by some Germans and was being used to pirate XBOX games. Took me hours to hack my way back into the server and the hard drive was packed full of games...
When Ultima Online came out, that was my first foray into "graphical MUDs", and like in college, I was hooked. Between that and Diablo, I had to have 2 phone lines... one for dial up and one to talk. Oh the good old days... From there came DAoC, which got more than just my few gaming friends involved.. that got my brothers and their friends involved too, and we could get 10+ of us on at any time, which was great. D&D Online was another one I loved because it was the first time D&D was done well. I ended up going back to that a couple years after release and got hooked for about a year. Lineage II was big for me because it started "the grind" - playing for hours on end to grind out one piece of equipment or one level. That game is one you could spend 1000 hours grinding just to get midway through levels and have moderate gear. It was also the first game I made money on, selling my characters for $800. Star Wars Galaxies was big for me because it was Star Wars where you actually felt like you were in that world, but also because I ran it like a business, and quit it because it was too much work (and the game was terribly buggy).. It was fun becoming the richest guy on my server, for a short time anyway.. Of course, WoW was great at first, because it was made by Blizzard, makers of Warcraft II and Diablo, but I played for barely a year and never looked back.
Around the same time as Ultima Online came Diablo, and OMG, talk about a defining game. I remember playing 4 way games too, which was great. When Diablo 2 came out years later I hated it at first, but nearly a year after release I got back into it with a friend and spent the next 2 years playing hardcore version daily until 2 am. It was the first game that hooked me for more than a few months.
I have played hundreds of PC games in between all these, but none really stand out more, at least not until League of Legends.. That one brought professional gaming into the mainstream, at least in the states (StarCraft was already huge for pro gamers in Korea). I stopped playing about a year ago though, started playing Heroes of the Storm because Blizzard, but haven't turned it on for a couple months...