One font or two? There are no rules particularly but it seems that either is acceptable. Three however is RIGHT OUT!
Seriously though, we find that most successfully executed book designs tend to utilise either single font or two contrasting ones. The first picture I have posted above is The Sunrise by Victoria Hislop. We can tell straight away that this is a romantic work of women's fiction. The colours are soft and the fonts, while contrasting, are fairly unobtrusive and work in harmony with the photographic background. The second photograph, is a work by Raymond Chandler, whose hard-boiled detective fiction has widespread appeal and pulls no punches. Here you can see the same font used to striking effect for the title and the authors name. This book cover is all about the stark typography. Both work well in clearly communicating brand and genre.
What else is the writing on the front cover of your book saying to your audience?
Apology: I currently have no information about who designed these two lovely jackets so my apologies for that. If I do unearth the information, I will add it here.