What kind of motors are used in bike?

There are electric bikes(which usually legally are considered bicycles) and there are bikes with combustion engines.(which usually are seen as either scooters/mopeds or motorcycles by the law.)
For the combustion engines you can have either 2-stroke engines(which usually are fairly small) or 4-stroke engines.
You can have one cylinder, or several. Then there are a few custom builds with turbine engines and the occasional drag/showbike with jet, or rocket engines.

Most bikes run on gasoline, but there are Diesel bikes too.