Quake 1 started it for me.... used to play it on the LAN when I was in junior high school. I was so addicted to it I played it every day for the entire one hour period. I got ridiculously good at the game and could kick everybody's butt. That carried on for years, until eventually I stopped playing as much, my reactions got slower and my movements got less precise.
I'm a FPS guy by mostly, some 3rd person shooters and the occasional racing game or flight sim. I've tried RPG's and other strategy games but just got bored too quickly. I like the effect that I'm the one who is on the front lines, in the thick of it. I don't care for commanding really...
Duke Nukem 3D was a fairly strong contender at the time of Quake 1. I played it a fair bit as well but didn't like it nearly as much because of the 2D sprites and a few other technical things that I felt Quake was superior. For awhile I had a few buddies who would play against me over dial-up modem. One would host and the other would dial-in. This sucked for me because since I was so damn good at the game I would have to dial-in and suffer with the lag or they wouldn't play. I remember upgrading from a 14.4 modem to a 33.6 and WOW! That was awesome and could kick so much butt so much faster!
Later in my youth and in high school I got a job and could afford to buy computer hardware. I was already interested in computers so I had made my own LAN at home. It wasn't long before I invited friends over and we started having LAN parties. This was back in 2001 and I'm STILL doing these.
Now I host 12-16 player LAN parties about every 4 months which is something I am always looking forward to. Unfortunately a lot of the new games are no longer being made with LAN hosting support so our days of LAN parties are numbered. We still play Quake 3, Far Cry 1 and 2 (and I hope 3!), Battlefield 2, Call of Duty 2 and 4, and S.T.A.L.K.E.R. All great LAN party games... Unfortunately the new Battlefield 3 doesn't have LAN, and shoving 5+ players through a 5mbit down, 512kbit up internet connection results in some problems trying to join servers.
I play a few 3rd person shooters as well. I played the original Max Payne, and then Max Payne 2. I think 2 was my favorite from a technical perspective. I just loved the mechanics and the way it felt to move around and shoot. I'm a bit of a realism junky too, so seeing the empty rifle and pistol magazines stay on the ground was kinda cool. Graphics are something I really enjoy too, I spend time in games to go slow in some areas just to admire and enjoy the scenery and details. I don't think a lot of people do that... they just plow through for the story and "accomplishments". I'm definitely looking forward to this new Max Payne 3, unfortunately I'm poor and won't be buying it until its on sale on Steam probably, unless I win it then I'll be playing it immediately.
I've played a lot of GTA 3, Vice City, San Andreas, and GTA 4 too. I've always loved the GTA games, having vehicles and gun battles in the same game, and being able to explorer a vast area always keeps me entertained for hours.
I could go on for another 20-30 paragraphs but I'm itching to try BF3 with this new patch that was just released! So, here's to winning! Cheers.