Everything I know about rotary engines can be summed up in one sarcastic sentence: "Hey, communism worked in theory too." That might be oversimplifying things: we can also add "boost goes in, apex seals come out" to the list while we're at it. It's safe to say that Felix Wankel's invention never really achieved the widespread popularity some originally thought it would, but it can't be said that the rotary doesn't have it's loyalists. Rotarys may be torqueless, thirsty, failure-prone, and oil-slurping emissions monsters, but they do sort of dominate on the racetrack.
This post isn't going to be a "how the hell does a Rotary work, anyway" post - there's Wikipedia for that. (Although ask and you shall receive, if there's any interest in such an article.) One of the greatest things about these engines is the sound an uncorked Rotary makes when it's being wrung out. So sit back and enjoy the dulcet tones of the Dorito Spinner, one of the oddest engines ever to find it's way into a production car.
This first video is an RX-7 so far from stock, it should probably be called an RX-10.5. It's actually got a 3 rotor engine (the 12a/13b were 2-rotors) made up of RX4/5 parts as well as a big T04B boosting at 20psi. This one looks extremely rapid.
Another triple-rotor RX-7 here, this one a third-generation (FD3S) with a Eunos Cosmo 20b 3-rotor boosted to kingdom come. The sound this car makes on boost is just nuts. Notice the welded differential in the back, too? Hardcore.
A 13b (2-rotor) 3rd gen RX7 drag racing in Trinidad(!) The legend of the spinning Dorito has reached far beyond Hiroshima, it seems. This thing takes off like it just got rear-ended by a dump truck. Insane.
I have to assume that when the apocalypse comes, it's going to sound a little like this. Oh lord. 7 second drag rotary is an impressive sight indeed. This one's another triple-rotor 20B in an FD chassis RX-7. How much power? Probably a gazillion.
Rotaries are so light and can make so much power they manage to find their way into all sorts of race cars they were never intended to. For instance, how about this 9-second Datsun 510 Wagon?
Ahh, a humble VW Beetle. Little air-cooled flat four, 50 horsepower, the People's Car... wait, no, drag monster with a turbo 13b in the back, pulling a wheelie on the bars halfway down the track. That's more like it.
The Datsun 1200: Datsun's competitor for the Toyota Corolla back in the 70's. A cute little coupe with a 1200cc pushrod 4, the original couldn't really punch its way through a wet paper bag. This one's been augmented with... yup, a turbo 13b rotary engine. It's starting to seem like everything is better with a little rotary under the hood.
If 2 rotors is good (13b), and 3 rotors is better (20b), then a naturally-aspirated 4-rotor in an RX8 sucking in air through 4 individual throttle bodies is the best. Right? Right.
I'm not the first person to point this out, but a Japanese car has only won LeMans once, and it was powered by a rotary. The 787B's 4-rotor 26B engine put out 930 horsepower (naturally aspirated!) in qualifying trim, and 700 or so in competition trim. If that's not a rotary sound to end a post on, I don't know what is. What else would you suggest?