Well, it kinda depends on what you define as a story.
I mean, I laugh at the number of posters here who say I HATE ALL STORIES THEY SUCK!!! butbillmaloneiscoolilovedsamthebellhop.
Christopher made a very good point about generalising.
But see, here's the thing. Basically all of our patter are stories. I mean, they may not be "This is a time machine" (Shanku, if you're reading this - sorry

) or "These jacks are robbers". But in some form, you're telling a story. Magic needs stories in some form or other because a card changing to another card, or aces transposing with kings, or a deck disappearing, by itself,
has no meaning.
As a mentalist, my performing persona is that of a student of psychology. Therefore, I often talk about real psychological phenomena that I apparently demonstrate. Granted, sometimes I go into more detail than other times, and vice versa. But regardless, even if I just mention it, I've giving my effect a story.
Of course, let's take a more obvious type of story. Let's take a story about a gambling routine. That's a trick with a story. There are lots of them. What about those? This is the problem with generalising.
Incidentally, anyone interested should also check out Daniel Garcia's impromptu version of Sam the Bellhop, it's brilliant. Also, Tony Chang's ACR has a great story to it.
Of course, that's not to say that some very valid points have also been made above - I think stories are fine, stories are necessary, even. But the problem with stories is the problem with a lot of patter in general - it just needs to be better scripted. It is true that scripts that are too cheesy will be boring - there are lots of them. There are also many scripts which comprise of "I'm now turning over the top card. And look, just one card, nothing fishy." Boring! But magic does need meaning - to that effect, don't be so quick to disregard stories - only bad stories.