That's a pretty tall order for any anthology. In my experience, no such collection is perfect - even a good one will have only a handful of good stories, the rest being mere page-fillers.
Stories is no different, despite Neil Gaiman's promises. Out of the twenty-eight stories it contains, about ten are actually good; another two or three are readable. I couldn't really find any reason for the addition of the others in this anthology - maybe the hope that the famous authors would attract more readers.
Some of the stories are mere sketches (Michael Moorcock's Stories, for example), others peter out halfway, leaving you feeling cheated (Roddy Doyle's Blood). Many are good ideas, half-heartedly executed (Kat Howard's A Life in Fictions). I got the feeling that they had been hurriedly written in order to meet an obligation or a tight deadline. At any rate, the editors don't seem to have done much filtering.
The story I enjoyed most was Joe R. Landsdale's The Stars Are Falling - a dreamy tale set in Texas that begins, "Before Deel Arrowsmith came back from the dead, he was crossing a field by late moonlight in search of his home." It's a twist on the typical zombie tale - one that involves lost hopes and mislaid lives.
Overall - you'll enjoy this anthology only if you don't let the famous names on the cover fool you. In fact, the stories written by the authors I recognized were generally disappointing (Neil Gaiman's The Truth is a Cave in the Black Mountains being the sole exception). Set your expectations low before reading this anthology.