Longreads: The Best Long-form Stories on the Web (so they say themselves). The site address is simply: http://longreads.com/ There are stories organized by a wide range of categories. You can search for stories and you can organize that search by story length rated by the minutes it will take to read them, which I find clever.
Gives Me Hope: Uplifting very short stories contributed daily by average folks. These stories will perk up your day and give you all sorts of little illustrations that can be incredibly useful. The site address is: http://www.givesmehope.com/
For a very different sort of story ... very different ... see this blog post: http://jsbrookspresents.blogspot.com/2009/04/survey.html