Gygax, for those of you who generally don't run in geek circles, was the creator of Dungeons and Dragons, the vehicle wherein a boy from the suburbs of Minneapolis could, through the easy-to-pick-up rules and a heavy dose of imagination, make the transition from awkward adolescent to shining hero with none of those messy intermediate steps in between (slayable orcs being something of a rarity in the Minneapolis suburbs).
Gygax's brainchild, derived from the addition of fantasy rules to a straight medieval wargame called Chainmail, spawned legions of imitators, some pastiches of the original concept, but more set in just about every genre available to fiction.
But the impact of D&D extended far beyond publishing houses with a taste for funny-shaped dice. Without the inspiration of D&D, there would be no World of Warcraft. The emphasis on encouraging the imaginations of the players also makes it a conceptual ancestor of Second Life, as well.
This would be a subtly different, but far less interesting world for the lack of Gary Gygax in it.