Happy National Short Story Month -- for another week! I'm a big fan of short stories. Lately the big thing seems to be connected stories, or a novel told in short stories (think Olive Kitteridge). Not that it's a new thing; Jhumpa Lahiri did it beautifully in Interpreter of Maladies (which won the Pulitzer Prize, as did Olive Kitteridge, by Elizabeth Strout) and again most recently in Unaccustomed Earth.
Sometimes people who think they don't like reading short stories just need some good suggestions. A good source for stories is the annual Best American Short Stories. The current edition (2010) was edited by Richard Russo, and the 2011 version, which will publish in October, is edited by Geraldine Brooks. I also like 20 Under 40: Stories from the New Yorker. Also try the annual PEN/O. Henry Prize Stories: The Best Stories of the Year.
Here are some other good collections: Nine Simple Patterns for Complicated Women by local writer Mary Rechner; You Think That's Bad by Jim Shepard, who just read here last week; Where the God of Love Hangs Out by Amy Bloom; The Boat by Nam Le; Gryphon by Charles Baxter; Saints and Sinners by Edna O'Brien; Last Night by James Salter (the last story always gives me chills); and Mrs. Darcy and the Blue-Eyed Stranger by Lee Smith.
There's a whole bunch more, but this list should get you off to a good start. Happy reading!