EtA: I've never read anything from other authors set in the Asimov's universe, so I have no opinion on them.
Roger MacBride Allen's Caliban
trilogy is fantastic.
/Robots and Aliens
-- I loved these when I was thirteen. That's probably the best thing I can say about them.
Robots In Time
Mark Teidemann's trilogy -- A sequel to Robot City
, but it seems to have been written by someone who never read Asimov because he truly misunderstands the Spacers.
I have not read Have Robot Will Travel
nor the recent Susan Calvin novel.
And Foundation's Friends
is worth it for Orson Scott Card's "The Originist." The rest of the book is pretty bland.