Super Mario World - First game I can really remember that was mine, on my first own system (rather than my uncle's stuff). I measure any and every platformer against Super Mario World, I haven't played anywhere near enough that hold up imho.
WarCraft 1 - Back in middle school I friend was excited to tell me about WarCraft, he sat me down with a pencil and paper and drew stick figures of the units telling me each thing they did. I got a copy of the game, played it, loved it, followed the series. And while I haven't touched many RTSs outside of StarCraft and WarCraft I can't imagine no longer enjoying RTSs if those two series go away (which I guess WarCraft already has).
Final Fantasy VIII - My younger cousin got into RPGs before I did, and seeing the fun he was having with one in particular (Final Fantasy 7) I thought I'd give it a look, but he had a playstation, and I didn't. So I found out FF7 was available on PC, tried the demo, a small room, where all you did was fight enemy after enemy, all it was really for was to give the player a sense of the combat, and I hadn't really played much quite like an RPG before, I adored it. I wanted it. My grandparents were going to the store, I begged them to pick me up Final Fantasy 7 for the PC. They came back with Final Fantasy 8, for some that would be a nightmare, but for one of the few times from around those years I accepted my game, gave thanks, sucked it up, and gave the game ago, and I love my Final Fantasy VIII to bits and pieces, and has lead to many other RPGs.
Mortal Kombat OR King of Fighters '99 ??? - I'm sure we've all heard about the controversy of Mortal Kombat's release, and I'm sure like a lot of you I was right in the middle of it as a kid. I got sucked into the controversy, rented the game, played it, loved it. It was my first fighting game, and the series responsible for me first picking up fighting games at all, though, leaving the series to itself it may have also been the series that kill fighting games for me. Babalities and Friendships shook my faith, the cornier and cornier characters turn me away from it, I was hanging by a thread with Mortal Kombat 4, then the only Mortal Kombat news coming out was for beat em ups and I walked away. My cousins continued playing them, I'd pick up one from them every now and then, but the games weren't the same any longer, and what was there before I lost touch with, I no longer cared for Mortal Kombat.
King of Fighters '99 though, on some odd chance I picked it up sometime after getting my PS2, and while Tekken 3 kept fighting games alive in the back of my mind, and Tekken Tag Tournament kept me happy and busy, KOF '99 got me to love them again.
TimeSplitters - Early PS2 must have title, and I had it, and it has ever since determined how I look at mutliplayer FPSs. While my favorite is Unreal Tournament 2004, I may not have gotten there without the first TimeSplitters.
X-Com Apocalypse - So back in middle school my friend tells me about WarCraft, I play it, I love it. A few months later I find in the store X-Com Apocalypse, I have no idea what it is, it just looks cool. So I get it. Take it home, play it, and become enthralled, I think my grades took a hit because of it. It's so amazing I have to show my friend, we trade games to borrow, and we never got around to trading them back. So, a few years later in a store I spot X-Com Collectors Edition. Play X-Com UFO Defense for the first time, and I find it to be everything Apocalypse was, only better, the graphics aren't as good, there's no real time combat option, but the world is bigger, the maps are more open, it's perfect, and the reason I've ever played any turn based strategy game since. And X-Com and Space Hulk taught me video games can be HARD.
Resident Evil 2 - My first Survival Horror game. I don't know if this should be Resi 2 or 1, 2 was the first, 2's the introduction, but 1, after playing 1 I new I wanted more, after playing 1 I tried 2 without cheats, after 1 I took 2 more serious, before 2 was a fun zombie shoot em up, but 1 with all it's cheesy dialog, it's bad acting, it's poor ass opening video, it was pure B-Movie goodness. Survival Horror gateway drug.
Resident Evil 4 - Resident Evil 4 was the game that taught me how to not feel anything, it filled my soul with darkness and then devoured it, it turned my insides into ash, it made me lose my innocence - OR it taught me to appreciate what I got, be happy for the games in the series I did enjoy, and people can love video games I do not. Before RE4 I'd hear people talking about games they liked and didn't like, and I'd disagree with a fair amount, but 4 took it to a whole new level, this was no longer people hating Final Fantasy 8, this was, for once, me not liking something, having thought out ideas as to why, being able to list them, and people loving the game all the while, as I waist time trying to understand how someone can like a video game so much that I have perfectly valid reasons for not liking, I had lists! So, yeah, it wasn't a huge shock, it was just so over whelming love for the game, it was my first taste into the many liking something that I do not, and not being able to fully understand.
the Bouncer - Where Resident Evil 4 taught me people can like things I don't, the Bouncer taught me people can look at the things I like and call them garbage, broken, and even sometimes in the middle of it stop making sense. The playstation 2 was the first console I had where I was always reading reviews of the games for. And the reviews I read about the Bouncer, they were negative. They were telling me (not really me of course) that the game I liked and enjoyed was BAD, that I liked a BAD game...but I like it ;_; (is that a crying face? cause it's meant to be a crying face). Then the other part of it was a review I read where the author/review was complaining that your AI partners in the game didn't do anything, that they didn't help that they don't do anything - followed two or three sentences later by the reviewer then saying the AI partners were horrible because they would steel your kills, well KO's but what ev'. It was a mix of wanting to defend my game, and understanding that people don't always make sense. the Bouncer taught me that not everyone's going to like the things I do, in fact sometimes they may really not like them, this would continue to hold true for the Resident Evil series and Final Fantasy VIII.
EDIT > Damnit, that's a damn essay. I need to learn to get to the point quicker.