#1 XCom. The UFOpedia is something I _loved_ in this game. The UFOpedia is one of the most notable items in this game, as it deeply detailed the in game stats of various equipment as well, as notes on the properties and suspected origins of the item--with rather well done images right next to the item being described. I dunno, maybe this is a sign of OCD, but I kind like knowing the properties of in game items.
#2 Megaman Classic|X|Xtreme|Zero|ZX -- all included as one game... because that is all it is... just repeated over and over. Sometimes with several episodes of it released in the same year. This is part of why the series was so damn unbalanced. I will not confess to being good at it--but I do enjoy putting it on every now and then.
#3 Cruis'n |USA|World . Yeah, these are generally regarded as horrible games. However, I love just how arcade like and cartoony their driving physics are. Hey, at least they are being honest. As most racers tend to botch up some very important physics somewhere. At least this has fun with the matter.
#4 Star Fox SNES . Well, Star Fox 64 is better, but this was the one that influenced me the most to love Rail Shooters. Put out a Rail Shooter, and well... I am likely to get it.
#5 Sim City. I loved this game as a little girl. Eventually I got good enough that I could get most of the scenarios to a successful level. I loved the amount of fun I could get with this game.
Notable runners up: The Commander Keen Series, Archmage (oooooold Browser Based Game), Quake I, Terran Legacy (oooooold Browser Base Game), Warcraft I, Legend of Zelda: Majora Mask, Super Mario Bros 3, Super Mario Bros USA, Wizball, TMNT 3: The Manhattan Project, Pango, Space Invaders, Super Solvers Club, Where in the World is Carmen Sandiego, Secret of Mana Series, Earthbound, Earthworm Jim, Super Smash Bros, Various Pinballs, Tetris.. but yeah...
Yeah, it was hard to make the most notable ones in this list, but here they are.
Also, as per why Pokemon does not even place anywhere on this list (as I know silly things like, the character Silver is actually Giovanni's son, I am prolly going to need to note why this is not an overly influential game on me (also, because for some reason I have gotten a reputation as an expert, even though there are many people who know way more about it than me)):
Other influences in my list that made Pokemon just seem logical to have came about regardless:
* X-Com... big time. Pokemon is just a cutsy Japanese cRPG revision of X-Com. They also did a very poor job on it.
* Megaman. I am fairly certain that the big concept of Pokemon could be easily be set as another form of "Megamaning" (those of you on TvTropse will be well aware of this Trope)
* Cruis'n USA. In that it does not really desire to be realistic in how it brings stuff. I mean, considering some of the large amount of Nightmare Fuel in the game that can be controlled by a 10a or 11a Boy or Girl (who uses them against Team Bad Guy), how is it possible to have a realistic scenario? At least they are being a little more honest than other games.
I mean Pokemon just seems to me to be a process that was long in the works >.>
I just wish most of the coding on Pokemon was not so failish--by both Game Freak and fans of the series >.>
BTW, tagging a fair amount of the runners up.