I'll be the first to tell you that short story collections don't sell well—it doesn't matter whether you've had short fiction in The New Yorker, it doesn't matter whether you earned your mfa at Iowa, it doesn't matter whether you're drinking buddies with the ghost of Flannery O'Connor—they uniformly don't sell very well. Often an agent will only take a short story collection from a promising new author on the condition that they also get his or her first novel.
However! The short story itself can be a way of grabbing an agent's attention, and getting yourself represented is half the battle. For example:
Publishing short stories lends you street cred. True, the agent is more interested in your writing than in your biography, but a biographical note that includes "Chester A. Author has recently published fiction in The Atlantic, The Paris Review, and The New Yorker" will almost certainly catch an agent's eye. That doesn't mean (s)he will immediately sign you, but (s)he might decide to send a request for a partial rather than a polite rejection.
Literary agents read literary journals. I know a few (and know of several more) agents who regularly read literary magazines in search of new talent. The more you publish, the higher your profile.
Literary agents recommend writing and writers to each other. Even if your dream agent hasn't read anything in which you've been published, (s)he still has plenty of friends, colleagues, and friends of colleagues who may have. Remember: a huge number of new authors are signed based on recommendations rather than via queries culled from the slush.
Publishing short stories entails writing short stories, and writing short stories entails a ton of practice. It goes without saying, but if you've written enough to publish several short stories in reputable magazines and journals, you've put a fair amount of time and effort into your writing. I've said it before and I'll say it again: patience and discipline are worth more in this business than talent and luck (though you'll need some of the former and a lot of the latter).
There you have it, amigos and -as. So now, prithee, inform me: which magazines/journals do you regularly read or subscribe to? Where do you find new authors? Which authors or stories have you read recently that you loved, were excited about, or recommended to others?