How to Drill a Square Hole

This type of engine is much more complicated and expensive to manufacture. Mazda owns a lot of patents dealing with heat expansion of metal alloys and other stuff related to manufacturing these engines. So they only put them in high margin cars, and stick with the old cheap engine for everything else.

Generally they are not especially efficient and have a problem with emissions. Because of their odd shape sealing them is much more difficult than a standard engine. By design Mazda rotaries burn a little oil to keep the seals fresh.

http://en.wikipedia.org/wiki/Wankel_engine#Disadvantages

They burn oil like mad to keep the tip seals of the rotor lubricated. They suck down gasoline - the RX8 gets maybe 15mpg if you drive it hard. 20 if you are careful. And it has to be premium. You have to be careful not to flood the engine - never run it for less than 30 seconds, or without revving to at least 3K RPM.

The upside is that the engine itself is tiny and mounted almost exactly in the middle of the car - under your feet. Rotary's get about 3x power for the same displacement as a reciprocating piston engine. They're great in airplanes.

I've spent a lot of time in an RX8 and it's a blast to drive if you're willing to deal with the cost and finicky nature of the beast. When the engine spools up and it just starts whirring... that's a beautiful thing.

Because Mazda enthusiasts (aka rotorheads) love them, and they are actually really good sports car powerplants.

But as other people have mentioned, they have some downsides, pretty much all due to their hard-to-seal and oddly-shaped "combustion chamber".

But nothing drives a following like an unusual design with inherent impracticalities (Cf. 45-degree V-twins, late-90's air-cooled Porsches, and Lisp ;).