The engine types are usually used in the following order, depending on the number of cylinders: I-4, V-6, V-8, V-10, V-12, W-16.
Flat engines are called flat because that is exactly what they are. The cylinders lie flat. Half of the cylinders are located on one side of the crank shaft and the other half on the other side. The advantage to having your cylinders horizontal is that the engine can be placed lower in the car. This makes the car more stable because of a lower center of gravity. Being lower in the also has a space advantage. The engine bay is far less crowded. They are found in porshes and subaru's. The are also known as boxer engines. Usually Flat-4 or Flat-6.
Inline engines have cylinders on top of the crank shaft. They stand inline at a vertical 90 degrees. Inline engines run smooth and can provide a lot of power. The engines, though, are longer then any other type. In cars today, most inline engines have small cylinders so length is not an issue. Above all, Honda's and many imports of today are known for their inline 4's today. Usually I-4 or I-6 for cars. Some marine engines have been made that use the I-Engine type with up to 14 cylinders.
V-8's and V-6's engine types exist today in many American cars and trucks. The cylinders are located on oppsite sides of the crank shaft and are elevated up a varying amount of degrees depending on the manufacturer. The V-type engine is known for using a pushrod valve system. Usually V-6, V-8, V-10, and V-12.
W-Type engines are found in few cars. For example there is one in the Bugatti 16/4 Veyron, which has a quad-turbo W-16, and there was a limited number of Volkswagen Passat produced from 1998-2005 with a 4.0L W-8. The Bugatti 16/4 Veyron's "16/4" is there for the simple fact of representing its engine. W-engine types work well for a large number of cylinders because everything becomes more compact and shorter. Though, they are more compact, the disadvantage is that they are hard to fix and more expensive to repair. Not many models made though the engines produce go up in multiples of four. The Bugatti Veyron engine is pictured below.
Wankel engines are also know as rotary engines. Wankel engines are completey different from any other type of automotive engines. It does not have pistons. Rather a single triangular rotor spins around a peanut shaped chamber. The triangular rotor is a special type of triangle also known as a Reuleaux triangle. This triangle has an equal diameter relative to the center at all times. The shape it is based off of an equilateral triangle. The reason this type of triangle is necessary is to ensure a seal during the triangles rotation at the center of the housing. There is a single straight shaft through the center of one of these engines that serves the purpose of a crankshaft in an otto cycle engine, otto cycle is the 4-stroke cycle in a regular pistion engine.
Wankel engines are found in Mazda RX-7's and RX-8's. Pictured below is a rotary engine.