Are there any pressurized piston engine-powered aircraft? Or does pressurization require a turboprop or jet?
The first pressurized aircraft were piston powered, beginning as early as 1921 with a modified Airco DH.9A containing a pressurized enclosure for the pilot. Throughout the 20s and 30s, pressurization systems developed in reciprocating powered aircraft with benchmarks like the Lockheed XC-35 being the first pressurized aircraft using bleed air from its super chargers to pressurize the cabin and the Boeing 307, the first pressurized airliner. World War II saw plenty of pressurized pistons like versions of the BF-109 and the Ju-86, as well as the Boeing B-29.
Postwar airliners were also pressurized. The Boeing 337, the Douglas DC-6 and the Lockheed Constellation were all good examples of this. With the introduction of jets, these quietly faded into obscurity.
There are a few pressurized piston single and twins in operation today, though manufacturers did not make very many.
Probably the most successful pressurized single is the Piper PA-46 Malibu series introduced in the 1980s and still in production today, in both the form of the reciprocating PA-46-350 Mirage and the turbine powered PA-46-500 and -600 Meridian.
In the late 70s and early 80s a number of manufacturers attempted to enter the pressurized entry cabin class single engine market. Cessna offered a Pressurized version of the C-210 Turbo Centurion called the P210 which is no longer produced but still popular with GA pilots today. Mooney, after finding marginal success with its pressurized M22 Mustang from the 1960s, decided to produce a pressurized six seat cabin class airplane called the Mooney 301. It was stillborn due to financial pressures from Mooney's new owners but the best technology from it was cannibalized in a ill-fated partnership with Aerospatiale (now Daher Socata) in Tarbes France to produce a single engine turbine airplane which eventually became the TBM-700/-850/-9XX (TBM stands for Tarbes Mooney).
More piston twins have been pressurized as well. Cessna produced a pressurized version of the C-337 Skymaster called the P337G, as well as the 340, 414 and 421. Piper produced the PA-31 Navajo. Beech produced the BE-60 Duke as well as a variant of the Queen Air called the B88. Rockwell produced the Aero Commander series.
Yes, both the Cessna P210 Centurion and Beechcraft Baron were pressurized from piston-powered engines. Going farther back in history, the B-29 was pressurized before jet-engine (or turboprop) aircraft were in production. So it is entirely possible for piston engines to give pressurized cabins.