Final Fantasy III (aka VI) - Played this when it first came out, think I would have been about 13. I had played a couple of the earlier ones, but they never really did much for me--I enjoyed them but they didn't stay with me. FFIII, however, struck a chord. The story sucked me in and it was the first time I'd ever really thought "wow, this isn't just a video game, this is art". The music in particular is what sticks with me--note that this was SNES, so we're talking 16 bit here. I can remember being floored by the amount of time that had to have gone into the music. Every character (there were many) had their own theme, cities/areas of the game all had their own music, etc--there was even a mini-opera:
http://www.youtube.com/watch?v=WwHrQdC02FYAnother bit from the same general part of the game, done by an orchestra/opera singers:
http://www.youtube.com/watch?v=7NC45S948ssKefka's theme--one of the better villains of any game I've played, and again another fantastic piece of music.
http://www.youtube.com/watch?v=4hqmeDtVEoEOne of my favorite area themes:
http://www.youtube.com/watch?v=t8CmlIhSf-U (the hissing I believe is because it was always raining in that zone, but I could be imagining things).
I'll leave that with a more somber piece:
http://www.youtube.com/watch?v=m69X198EAxk(this has made me want to go dig my SNES out of storage and play this again btw, though I don't even know if my flatscreen TV has a coax input)
So yeah, you can tell that FFIII/VI tops my list by about 10 miles.
Tetris - Got it for the Nintendo probably right before or after I moved to Argentina when I was 9 (1989-1990). My father and I used to play and compete for highest score, and I kept the NES even when I had an SNES just so he and I could play this game. We played all the way through until around when I hit high school. In college, they released a 4 player version for N64, so I got it and my friends and I used to play this while drinking/smoking/what-have-you on nights when there weren't parties or other things to do. Good times. And of course, the music. My favorite bit of it--complete with the sped-up version for when you fuck up and let the blocks stack too high, as though you aren't already stressed out at level 18 when you make an oops and you have to make instant decisions on what to do to avoid losing--goes until about 2:00:
http://www.youtube.com/watch?v=AHEs5kDwuck&feature=player_detailpage#t=25sIncidentally, an absolutely fascinating BBC documentary on the history of Tetris:
http://www.youtube.com/watch?v=Fn9dO_iL7lo Part 1 of 6.
Yikes. That's only 2.
Diablo II - Sucked me in later in college. Junior and senior year, several friends of mine and I would play together over the college network. It wasn't until I graduated from college that I started playing online, but once I did, through a forum (the first I'd ever registered on, incidentally--I later ended up as a moderator on the sister WoW forum), diabloii.net, I "met" quite a few people that I wound up playing with. This is where I first discovered the hilarity of griefing, incidentally. Bots were common on the ladder, and they would create open games to run the end boss of the game for XP--the more people in the game, the more XP, so they'd be public. The bot would use a maphack+teleport ability (sorceress or attainable through a runeword item and thus usable on any class) to get to the final boss, open a town portal, and everyone in the party would hop through and kill stuff. As soon as it was over, the bot would leave the game and create a new one with the same name, #2 or whatever, and so on endlessly. So we used to emulate bots, set up these games, get people comfortable, and then I'd go and find the nastiest most devastating spawn I could find, and open a portal right in the middle of it. Everyone dies. The fun part is, dying in D2 in hell mode had an XP penalty attached to it, often harsh enough that it would set you back several runs worth of XP. Some of the others in the group, also friends of mine, would convince people it was just a glitch with the bot, they ran with it all the time and it only did it once in a while. A few games later, I'd do it again. And so forth. Yes, I'm a bastard. But fuck people who ran bots/ran with bots. In any case, eventually through those same people, I came onto my first true MMO:
World of Warcraft - Yes, I played. For years. My first MMORPG, as I don't really count Diablo since I played for so many years in single player mode or with friends in the next room in what amounted to a LAN party. Still log in once in a while and tinker around. Formed a guild out of a dozen people that I knew through the diablo forums, and within 6 months we'd built a guild of 100 or so people and were setting out to raid. I was at the helm, and kept the guild running through 300 people and 3 years (it's now 6 years old and counting, though in the last 6 months or so it's finally winding down and dying) before passing it off to another friend. I met a few dozen people through WoW, and had two roommates that I met originally through the guild who later moved to my city and needed a place to stay. A few more traveled to the US for the first time on my sponsorship for a visa (apparently South Africans need a sponsor) and my couch as their place to crash (I was in the Washington DC area at the time, so was a good place for them to visit). I traveled three times across the country for guild meets, and eventually found EVE through another player in my guild, Scorpio Dantes as he was known in EVE. He was another office of the guild. Incidentally, he's one of the many members of the guild that I've met and hung out with, though he and I never did get around to going fly fishing together, it might happen still--he only lives about 5 hours away from me right now. In any case, WoW was the first game that introduced me to the idea of making real friends via the internet, and I made lots. Still in touch with quite a few, and wind up visiting with some of them when our paths cross. Oh, and the guild was known for being a bunch of drunken trolls.
EVE - Has to make the list. Same idea as WoW--I've made dozens of friends through EVE. Got a job through a friend I made in EVE (Aeaus). Have met dozens of my EVE friends as well on my travels. And as far as the gaming experience goes, I've played now for 5 years. Consistently through the years as well, unlike most of my other games that are hot and cold for me. And finally a place where my griefing was acceptable. \o/ The PvP was intense, unlike WoW or D2, and the game environment was harsh as hell. No respawning at the graveyard and running back. Your ship explodes, everything on it vaporized or looted by the winner, and you're back to square one. I don't really need to explain it I guess, we all play. But yeah, EVE is certainly in the top 5 of the influential games in my life.