There are some CS props that can be reversed, but they are not particularly common.
There used to be a couple of other variable-pitch types. One was a two-position (climb or cruise), and the other was ground-adjustable (adjust the pitch on the ground, and it stays the same pitch throughout the flight).
They’re pretty much universal on turboprops, which is just about all you’ll see commercially. I don’t know about the numbers breakdown for piston engines, but I know that both types are common. Reversible pitch props do exist, though again I don’t know what the percentages are.
Think of driving a screw - which is pretty much what a propeller does. If the screw has a fine pitch, meaning a low angle of the thread to the axis, it won’t go into the wood as far for every turn of the screwdriver, but you can make it turn with an amount of torque that wouldn’t turn a coarse-pitch screw. You need to apply more torque into the air when you’re climbing than when you’re cruising, to pull the plane up, so a fine pitch works better then.
In cruise, you want each turn of the prop to pull the plane farther forward, just like you’d want each turn of the screwdriver to move the screw deeper into the wood, given your choice. That lets each drop of fuel pull the plane farther - so a coarse pitch is better for cruise.
That said, planes with fixed-pitch props can typically be equipped with either climb-optimized (fine pitch) or cruise-optimized (coarse pitch) props, depending on the intended use of the airplane. A climb prop will be less efficient in cruise, and have a lower top speed too, but is a better choice for a trainer that’s always doing landing patterns. A cruise prop won’t let the plane climb as fast.
There are motor gliders with single-blade props for more-compact engine stowage behind the cockpit. They have counterweights for mass balance, but the center of thrust does orbit around the engine centerline, so there’s still some vibration imparted into the airframe and stick.
The “Thunderscreech” was reputed to be able to induce diarrhea in ground crew members.
C-124 Globe Masters had reversible props on it’s P&W 4360’s.
You could melt an engine in about 20 seconds flat in the summer time trying to back them on the ramp…
On my swift, I had a Beech Roby prop which was adjustable with a crank in the cockpit.
http://www.notplanejane.com/beechcraft.htm
http://www.rootsweb.ancestry.com/~txtarran/places/kennedy.htm
In boating, more blades on the propeller generally increases power. If you want to pull six skiers with four people in the boat, you’d put on a three-blade propeller. If you just want to take a boat-ride or go fishing with a few people, you might use a two-blade propeller for speed. I’m guessing the same principles apply to aircraft? Hope this helps…
Others have covered the outline of various prop types. Here’s some info on prevalance …
Fixed pitch props are only used now on very small light simple airplanes. 2-place homebuilts, 1950s & 1960s small Cessnas, ultralights, etc. They were state of the art up until the 1930s or so.
Constant speed non-reversing props are univeral on bigger piston lightplanes, such as 250+ Hp singles, and pretty much all light & medium twins. Back when military fighters had piston engines, they had constant speed non-reversing props. Pretty much anything built from the late 1930s to the mid 1940s had these.
Constant speed reversing props came into use on airliners, transports & military bombers about the end of WWII when tailwheels gave way to nosewheels. And pretty much every piston heavy thereafter had constant speed reversing props until they became obsolete.
As noted above, constant speed reversing props are universal (or nearly so) on turboprop airplanes. A few turboprop singles have an almost-reversing prop which can go to a zero-thrust flat-pitch condition but not actually into reverse thrust. This feature is commonly called “beta thrust” or “beta range.” The prop blades are flat to the airflow, and knife-edge to their plane of rotation. It produces a bunch of drag.
Most constant speed props, reversing or not, also have a position called “feather”. It’s the opposite of Beta. In feather the blades are knife edge to the airflow & flat to the plane of rotation. This setting is used when an engine fails or is shut down. It produces the least drag. It’s the aeronautical equivalent of coasting in neutral in your car.
Johnny L.A.'s wiki link does a decent job of explaining how they work mechanically.
A small price to pay in the world of flight test. Everything I’ve read about that plane makes me think we’re damn lucky it didn’t kill someone.
I did an internship at the company that built floats for Cessna Caravans. I don’t know if it can go into reverse thrust, but I have to think that backing up on the water would be a bad idea.
There is some interesting info under scimitar propsand propfans.