The Wankel rotary engine has been used fairly extensively for two purposes: as a compact portable petrol engine for items like generators, small off-road vehicles, etc., and as an automotive powerplant. The first production cars I know of that used this engine were the NSU Spider in 1964 and the NSU Ro80 in 1967, but they were followed by a long series of Mazdas, starting with the Cosmo in 1967 and the R100 in 1968, followed by the whole RX series up through the RX7. I can recall test-driving an R100 when they were first produced, and being underwhelmed - I've never driven another car with as much clutch slip when power-shifted. Also, the Wankel engine was very smooth but severely lacking in low speed torque (which was probably the reason Mazda expected to get away with the inadequate clutch capacity).
At one time General Motors and many other car makers took licences to make the Wankel engine in huge numbers for small cars, but at almost the same instant, emissions controls became mandatory and the concept became undesirable.
I think the Wankel engine is now only found in applications where fuel efficiency, durability and exhaust emissions are less important than light weight and small size. Portable generators to be air-dropped by the military might be among the more important examples. It would be a bit expensive for a lawnmower, and rather a pain to overhaul, but otherwise that is probably a reasonable application. Sachs has been making Wankel engines for decades, selling them as multi-purpose powerplants in the same way as Briggs and Honda sell small engines.
