Percon, I disagree with you. That's a dangerous statement to make, because all sorts of people have all sorts of different thoughts about what a "story" is. If you mean only to discourage walls of text between levels of space invaders, then... well, okay.
There are times when the context, potential emotional connection, and sense of extrapolated space and time of pieces of story--or, frequently, well-used 'story elements' (i.e. THEME SETTING PLOT CHARACTERS! I REMEMBER GRADE 10 ENGLISH CLASS)--can really hit home and make a game feel that much better.
So, ah, still: I, too, think story should be approached in an "all or nothing" kind of way, but that shouldn't mean "make a game that's all about story or don't touch story with a ten-foot pole". Just don't half-ass it.
(That's not saying much, though, because it should probably be understood that unless you want to half-ass the game, don't add anything to it you're not willing to full-ass.)
Fair enough; I guess I was being a bit too extreme in what I was trying to say. If the gameplay comes before the story, though, I would hope that the developers don't compromise any part of the gameplay for a halfhearted story.