Stories: All-New Tales is very nearly the perfect short story collection. It's a very eclectic collection; there are fantasy stories, horror stories, science fiction stories, and general fiction. As Gaiman says in his introduction, the editors wanted to put together stories that are designed to make the reader ask. "...and then what happened?" Almost all of the stories do this and do it well.
Notice that I said almost. There are two exception to this. Chuck Palahniuk's "story," "Loser," quite frankly sucks. I would barely even qualify it as a story. It's about a frat boy on acid who goes on a game show that seems to be The Price Is Right as written by someone who's never actually seen the show. There is pretty much no action at all, and nothing of any interest whatsoever happens. Also, it's written in the second person present tense, which is really annoying.
The other exception is Michael Moorcock's "Stories," which is at least a story, just a boring one. This is rather surprising coming from the man behind the Eternal Champion series, since I know he can write a good story (I've never actually read anything by Palahniuk). This is a long rambling story about the life of an editor and his slightly nutso writer friend written as a sort of reminiscence. It's not really very interesting.
The rest of the stories range from great to pretty darn good. Gaiman's "The Truth Is a Cave in the Black Mountains" is excellent, as you would expect from a writer of Gaiman's caliber. Walter Mosley's "Juvenal Nyx" has great potential as a series character. Joe Hill's "The Devil on the Staircase" is written in a format similar to concrete poetry, but is a very good tale. Al Sarrantonio's "Cult of the Nose" is a great weird story. Really all of the other stories are good. Most of them could very well have been the stand out story in any other anthology. I wouldn't be at all surprised to see this being nominated for--and probably winning--several awards.