A story that requires backstory hasn't started from the proper beginning. Or, to put it another way, a story with backstory is told out of chronological order.
The reason for writing out of order is most likely because of drama. Either the backstory is so uninteresting that it ends up getting tucked away into other more interesting parts. Or, the backstory is so interesting that it's saved for the climax. In this latter example, the backstory serves to fill in a missing gap in the story, giving the piece as a whole almost a mystery-solving characteristic.
I'm not advocating writing everything in chronological order. Not at all. But, I do think that a story without backstory is a significantly different animal than one that does have it. A story without backstory carries a lot of momentum behind it. The forward-moving timeline really propels the reader forward, and I think it can have a much more exciting feel to it.
I also think that backstory often comes from an attempt to explain a character. In the "literary" character-driven-type story, a character's motivations often stem from some past experience. At least that's how I've used it. But, I wonder if this is also a limitation. It seems to me to be a rather narrow view of psychology when my character eats his lover because of some past break up he had while living in Paris.
What do you all think? Is backstory a weakness? How many of your works don't have backstory? And, most importantly, does it matter?