I think it really depends on the type of game, RPG yes, most important element really(you not playing one for the same gameplay mechanics in a different setting are you?). Strategy, pretty important, but you should work on other things first(like gameplay). Shooter, i would like one but i can last more than half the game trying to find different ways to shoot the same gun, which should be there if you want me to buy it) MMO, no i'm fine playing with others without a story. And Puzzle, a bad story could hurt a puzzle game while a good one probably won't help alot, unless your Portal-style, because those ones are the only puzzle games i buy.