Book One of Incarnations of Immortality
The story of a 'regular guy,' Zane, who after a run of bad luck, decides to commit suicide - but instead, as Fate would have it, is picked to assume the office of Death. The job comes with any number a perks - a shapechanging Deathhorse, a manor in purgatory, and who knows what powers - Zane needs to figure that out as he goes along, collecting the sould of those whose lives are in balance, neither good nor evil, to be sorted out and sent to hell, heaven, or purgatory.
To complicate things, there's a pretty girl, Luna, whose magician dad has tried to engineer things so that Zane would get together with her - and of, course, an ongoing struggle between god and Satan - and Satan seems to be cheating.
This is an entertaining-enough light fantasy read, but it also has pretentions to "pointed social satire" as Anthony says - which aren't really that pointed. The characterization is slight, and it also seemed slightly sexist. The cosmology is also very simplistic.
Four years later than this book, Terry Pratchett published his humorous fantasy book about Death (Mort), which shares a LOT of similarities with this book - and although it might have come later, it's just much much funnier and better-done. If I hadn't already read Mort, I probably would have liked this much better.
At the end of 'On A Pale Horse' is a rather long 'Author's Note' in which Anthony talks about some of his aims as a writer and his life at the time of reading the book - and it's a really interesting, attention-grabbing essay. Ironically, it might have been my favorite part of the book!