I would call myself a Gaiman fan, but it really is a case of completely accepting the central premise for each of his books at the start for the story to 'work'. If it doesn't grab you straightaway then they can read as a writer trying to be clever, rather than actually being clever.
I havent read Anansi Boys, but have read and enjoyed Neverwhere, American Gods and The Graveyard Book. How cool is it that we each enjoy different authors, books and styles of writing and can always find others that feel the same about them?