Sure, why not. I'll jump on this band-wagon.
Here are the fifteen games, in no particular order, that have inspired me the most:
AD&D - Forgotten Realms
AD&D - Spelljammer
AD&D - Masque of the Red Death
AD&D - Birthright
Vampire: the Masquerade
Mage: the Ascension
Star Wars d20
Hearts of Iron II*
Call of Chtulhu
*Since Trey over at the Sorcerer's Skull listed an FPS, I figure I can include an RTS.
** A crappy Facebook game that still had me chained to the pooter for almost a year.
*** I've never actually played these games, but they have still left an imprint on my mind.
As you may be able to infer from this list, I came into the hobby in the early nineties.