Are there any "Fantasy Passports" that are recognised by other countries?

If you define "fantasy passport" as a passport of a country which isn't fully internationally recognized, then I believe the Palestinian Authority passport would qualify. Which in fact is recognized as travel document by some of the countries, which don't recognize Palestine as state itself.

What exactly is your definition of "fantasy passport"? Most obvious definitions already answer the question. And what exactly does "recognise" mean (the World Passport wikipedia page says that there are official documents from some third world countries that confirm its acceptance, but with dubious current validity)?

As an extreme case, consider Taiwan and China - the two governments each consider the other illegitimate and the issued passports invalid - while they are accepted in most other countries (including those that don't officially recognize Taiwan), travel between the two countries requires different documents that maintain the fiction that there is only one nation.