Hmm, well I think I'll have to change this a little bit because the question was games that affected me...to be honest, computer games have been a late addition:
Majiang from back in China is probably the most addicted game -- it isn't your matching game but a tile game with suits that plays much like rummy but you get money. I was a majiang-aholic.
Tennis -- I just played it all the time
In the States, I was introduced to:
Command & Conquer (the first computer game) -- this game was a blast and my boyfriend and I would play missions taking turns and teasing each other. And loving to hear the female commando's "CHA-CHING!" when she blew up a target.
Star Wars the rpg -- this is actually where the original idea for "Jinx" came from as it was my character's callsign. She was an X-wing pilot and a lot of fun to play with the group we played it with. I even spotted the Japanese girl in the crazy flightsuit on the web and it was perfect for the character's image.
X-Com UFO Defense -- nobody mentioned this computer game at all! I know it's old I guess but you're a secret agency established to protect earth from alien invaders, from the big eyed aliens to more exotic and horrible things. You created individual soldiers who were like your investigation and defense teams. Your inteceptor would shoot down a UFO and you would investigate with that team. Then you controlled them as a squad, action by action, and it was so tense. And I really got hooked -- I had favorite characters and they developed in skill as you went, and you hated to see one die... Anyway, nobody mentioned it but it's an awesome game if you can find it.
Silent Death -- back when we were up in South Dakota, we pulled out this space fighter boardgame out and we had friends over and all played. I got hooked and we had weekends where we all played out on this giant black cloth space map on the floor.
X-Wing Alliance (back to the computer) -- maybe because of Silent Death, I got into the Star Wars flight simulator; played TIE fighter too which was neat. Of course, I was Jinx.
The Sims -- ok, I'm sick -- lol! I got addicted making up these people and living their lives for at least several months and again years later with the Sims 2.
And of course...my first online role playing experience, SWG. At first I was just playing the game to explore the beautiful Star Wars galaxy, and hardly being much in character. But I think probably within a month, I was always acting as Sepiv "Jinx" Cithe and enjoying any chance to improv.
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Like I said... wish they'd re-release exactly as it was with better graphics for the XP platform! And, I did play Silent Death.... but I was more into Star Fleet Battles! Gobs and Gobs of stuff to go over! Remember, always save up for an impulse turn 'and' target their bridge!! Muahahahahaha!!!! 
