I've read a small selection of his flash fiction and some excerpts at this site: http://www.eskimo.com/~jessamyn/barth/
Some of my favorites hosted at that site include “The First Thing the Baby Did Wrong...”, “At the End of the Mechanical Age”, and certainly “Some of Us Had Been Threatening Our Friend Colby.”
His stories are written as if they were very serious and powerful fiction, but the ideas are often glib and amusing. Because of the brevity of the stories featured on the webpage, they can seem haunting and oblique. It often seems as if there are hints to some sort of meaning but all the important words or phrases have been cut out of the story.
However, though I have not read the novels, looking at the excerpts included it seems as if they have the same mysterious quality to them as the short fiction in addition to a more profound “post-modern” playfulness. Snow White includes a “quiz” (really more of a survey) on the reader's attitude towards the story, as well as his or her reading habits, for the reader to fill out.
While “post-modernism” is a phrase I found exciting as a freshman in college, by graduation it had become irritating. I think that a lot of people take up post-modernism to claim some sort of intellectual authenticity or braggadocio. One thing I find refreshing about Barthelme's work is the sense of humor he has towards his own writing. Some authors can write and the most you get a sense of is their own ego.
He constructs absurd situations (such as the ones in “The First Thing...” and “Some of Us...”) which are simply funny, and I think even the stories written in serious tones have a degree of melodrama that I would almost say hints towards a sort of satire. What exactly is being satirized, though, I think is debatable. It could be the type of drama found in fiction such as humorless novels or soap operas, or it could be the type of drama we might encounter in our real lives with humorless friends and acquaintances.
There is, actually, some real-world intrigue, besides his fiction. When Dan Rather was assaulted outside his apartment building in 1986, the man who committed the act had supposedly quoted a line which appears in a piece by Donald Barthelme, as well as some other striking parallels. The whole thing is explored in an article written for Harper's: http://www.harpers.org/archive/2001/12/0075777
So, I wonder if I can really say that I'm a fan of Barthelme. I feel like one. I should probably just buy a book or two of his and stop worrying.