The Danforth Review has a great Look at Fiction Online, an article that could serve as a good introduction for people who wonder where quality fiction lives online. I was particularly happy to see the marvelous Failbetter.com listed first, though I'm horrendously biased in their favor -- editor Thom Didato not only published a story of mine once, but then nominated it for a Pushcart Prize. (I thought about quitting my job and living off the fame for a while, but decided against it.) Thom also gave me my favorite rejection once, saying, "This is like broccoli. I know it's good for me, but I don't get much pleasure from it." Go read Failbetter. No broccoli.
The science fiction field is, of course, at the forefront of the online fiction world, with a site like SciFiction publishing some of the best work in the field -- a nice mix of new and veteran writers, various styles of writing, and phenomenal pay rates. Strange Horizons is also often good, and, among the younger online venues, Lenox Avenue and Fortean Bureau have shown themselves to be very much worth checking out. (A more comprehensive list is available at Locus.)
There is still, I think, a bit of a stigma attached to publishing online, though that stigma grows weaker every day, and it should, because the medium used to publish something doesn't matter; the editorial process does. Good editors who can attract and shape good material are what matter, and some of the online magazines have excellent editors who have found a certain amount of freedom with online media, and they deserve to be celebrated and supported.