Another resource that people might find interesting is
http://www.fiftytwostories.com/ which is a Harper Perrenial site which publishes a free short story weekly. They recently had the Neil Gaiman one from the 'Stories' collection I previously mentioned.
If you look down the bottom of the page there are a list of short story collections, I clicked through a few of them and they all seem to be available directly from Harper as epubs. Collections rather than anthologies but there might be something there of interest.