I'm curious how many patents there are for devices that are impossible to actually build. You know, fun stuff like warp drives and time machines.

Presumably zero. Patents are only permitted for "useful" subject matter. Useful is a term of art: you can still patent silly things like Slinkies: http://www.google.com/patents/US2415012?printsec=drawing – but whatever you patent has to actually function as advertised. So while the Slinky is objectively useless, it does what the patent says it does. A warp drive would be objectively useful, but when you build it, it won't do what the patent says it does; therefore, it's not patentable.

Though not quite in practice of course. I cannot substantiate my claim with data, but have come across several (approved) patents which are actually not even correct -- the described does not function as advertized.