I know there are different types if engines. All with different set-ups and designs. But do most engines have a cylinder head? And how many? I know inline engines have one, V-lines have two and radial engines usually have one for each cylinder.
All piston engines must have a cylinder head. The head is on top of the block and forms the top of the combustion chamber. The head is also where the valves are. The valves and chambers in the head allow air/fuel to enter the combustion chamber and exhaust to leave the combustion chamber. The head is removable to allow for assembly and maintenance.
As @rpmerf says, virtually all piston engines have at least one cylinder head.
Most engines will have one head per bank of cylinders, as you suggest, though some have more - IIRC some of the aircooled VW engines had one head per cylinder.
There are however some that don't have any - in opposed-piston engines, such as the two-stroke Napier Deltic and the Commer TS3, each combustion chamber is shared by two opposing cylinders, so each effectively acts as the head for the other. These will then have the valves in the sides of the cylinders.
If you want someting even crazier, have a look at Free Piston Engines, which don't even have a crankshaft...
Common piston engines all have cylinder heads (in the sense of a removable component that closes off the cylinder bore opposite the piston forming the combustion chamber).
All internal combustion engines need "something" like a cylinder head to provide something for the expanding gasses to push against and cause the piston or rotor to move – but that "something" doesn't have to be the conventional head that we usually think of – it could be another piston in opposed piston designs (which are used in heavy industrial and marine engines, the Fairbanks Morse 38 8-1/8 diesel engine is still in production), or the head and block could be a single unit, and then there are rotary engines…
A reasonable person could argue that the "non-head" designs are not "common engines." However one of the wonderful things about machinery is the way it displays the range of human creativity and design possibilities. It is also cool the way designs that once seemed to have died out come back.
Having a separate cylinder head make the manufacture and assembly of an engine much easier.
In particular it is much easier to bore the cylinders straight through a cast block than to attempt to cast and machine a block with blind holes. Similarly a separate head allows the pistons and connecting rods to be inserted from the top.
Most modern engines have overhead valves, this allows for the largest possible inlet/exhaust port area and the most direct path to the combustion chamber. This would be extremely difficult to achieve without a separate head. Similarly a separate head makes it much easier to manufacture a hemispherical combustion chamber.
Having a separate head allows the compression ration to be adjusted by either machining the head or changing the thickness of the head gasket.
It allows access for maintenance of valves, pistons etc.
In side valve engines the cylinder head may be little more than a plate
A separate head allows more development flexibility as the design of the valves and combustion chamber can be changed significantly without resigning and retooling the whole engine. You also have the option to manufacture the head and block from different materials.