Last week I had the privilege of hearing Julia Elliott read at the University of Maine's New Writing Series. Her story, from the Georgia Review, knocked my socks off. It's reprinted in Best American Fantasy despite being devoid of fantastic content; perhaps it is a bit associational, but whatever. A terrific story. Worth buying the book all by itself (and as a bonus, the rest of the stories are swell, too).
Here's a story of hers at the Mississippi Review: "Jaws"
And while we're on the topic of good online fiction...if you're looking for a place to start finding stories, this list from StorySouth (also this one and this one...) would be a good place to start.