Great idea for a topic. For me it's:
Jet Set Willy. One of the first games I played. Got my Spectrum +2 when I was about 6 and mostly played free demo tapes from magazines (I was too young to actually complete games for the most part anyway) but this one I bought with pocket money. You couldn't actually complete the initial release due to a bug but I was never even close, it was hard as fuck at points. The exploration was so new to me, discovering new rooms, finding out you could go to the moon (no internet to tell me), it showed me just how compelling gaming could be.
Super Mario Bros 3. When I got my NES for Christmas 1990 it came with SMB, Tecmo World Wrestling and this gem. I had dreamed of playing Nintendo for a while, growing up in the 80's and watching stuff like The Wizard, it was so exotic when compared to the Spectrum I had been playing until then, those massive cartridges, the graphics, no loading times... SMB3 was probably the first game I ever completed, it felt like I had been on an epic adventure and was around the time I started to see gaming as a means of escapism.
Doom2. We got the PC in 1994 as my older sister needed one for her GSCE's and I was straight in there with Doom2. The giant cardboard box full of floppys (DOS version) took a while to install but once it was running...It was cutting edge compared to the NES / Mega Drive era games. I still love the atmosphere, their attempt to make post apocalyptic citys using the tech at the time seem quant now but back then it was incredible.
Morrowind. I played this on the Xbox, it was my first proper RPG and certainly the first truly open world game I had played. I must have put 500 hours in, if not more, it totally absorbed me, I used to spend my days at work thinking about what I was going to do in Tamriel that night, rob the vaults at Vivec? track down more Deadric armour? Hunt in the wilderness? It's not aged so well, even with mods but it's still the best ES game and arguably one of the best RPG's of all time.
WOW. 5 Years of my life, some great online friends who I still miss interacting with and arguably my swan song to "real" gaming. I grabbed WoW on impulse in 2005, playing it casually and re-starting so often I thought I would never get to level 40, let alone 60. Then I took a year off and went to Australia (I had money to last me a year in relative comfort). Well that was it for me, between hanging out in the sun and with friends I had plenty of time and just about sufficient internet to get my way to max level. By the time I got home I was in a raiding guild and Burning Crusade had just hit. I had fallen in love with the freedom, the art direction and world building, I really liked some of the guys in the guild and we spun the shit on vent into the small hours while dicking around in game.
Sadly, I burned out and quit around the Lich King era, by the time I dipped back in the guild had gone and most of the people I liked vanished to Horde side / new realms. I kept trying to come back but the spirit of the game was gone, the social element / exploration was being replaced with Finder's, people just sat in queues in the citys waiting for things to happen.
I have never really got into anything since, I now mostly play Hearthstone on the iPad, the PS4 gathers dust largely, my wife's expecting twins so I don't expect this to change. I keep an eye out for anything that might scratch that itch again but I probably should accept it was a product of the time when I was young and free enough to live in Azeroth in it's prime.
Notable mentions: COD4, Streets of Rage 2, Treasure Island Dizzy, Warcraft 2.