"Paying It Forward" - Michael A. Burstein
Shame this is the first on the list. I really didn't like it. From a variant of the many interesting parallel world theories that are flying about these days (specifically Max Tegmark's) a dull story is poorly realised in clumsy prose. The central theme is the familiar relationship between wise old mentor and pupil which may appeal to others more than it does me.
"A Study in Emerald" - Neil Gaiman
From the first half page, which references Lovecraft and inverts Sherlock Holmes, while marching the story briskly forwards, you know you are in the hands of a craftsman. Victorian pastiche-SF (on the lines of the League of Extraordinary Gents) and eldritch horror. Not usually my type of thing, but I thought it was the best story of the set.
"Four Short Novels" - Joe Haldeman
Very short, sketchy, idea-centric SF. SF not even trying to be like 'proper' literature, and why should it? Cynical thoughts on immortality. I liked.
The Tale of the Golden Eagle" - David D. Levine
Elegantly written, stylised, old-space-empire story. There was nothing here I haven't read before. No strong feelings either way.
Robots Don't Cry" - Mike Resnick
Robots may not, but tears seeped out as I read this, while waiting for my daughter to have a hair cut. Emotive but terse. Worked for me.
Anyway. you can read them for yourself and disagree with me if you like.