Spin-Offs: The Good, the Bad, the Unrecognizable

When it's time for a popular series to come to an end, the decision is sometimes made to extend the story by creating a new show using secondary or background characters. Sometimes these efforts are a success ("Saved by the Bell" was a bigger hit than "Good Morning, Miss Bliss"); sometimes they could/should have worked but didn't ("The Lone Gunmen" from "X-Files"); sometimes they were ill-conceived from the start (why was "The Raven" spun-off from "Highlander" and not, say, "The Joe and Methos Show"?).

Why do some spin-offs work and others crash and burn? How do the elements of setting, story, characters, and actors combine to create something fresh and exciting from a fading star? Are there spin-offs that might have been successful on their own merits if they weren't being compared to a beloved predecessor? Are there examples of shows that were more successful than they merited, due to the reflected glow of their source material? Are there spin-offs-in-name-only that bore so little resemblance to their original shows that they were unrecognizable as being part of the same world?