There are a wide range of materials a car body can be made of, depending on the application. Many are made of steel for strength, or aluminium for strength with a lighter metal, but many high performance cars are made out of either fiberglass or carbon fiber components.
Steel
Steel is a commonly used strong metal which can be a little heavy, but less likely to dent from minor impacts. It is used commonly throughout the entire car, not just the body. There are many alloys of steel with varying weights, strengths, and costs.
Aluminium
For a lighter metal, aluminium is sometimes used. While weaker and more expensive than steel, it still has a decent amount of strength and is much lighter, which is appealing when making a performance car, where acceleration and handling are desired. Keep in mind, however, that the alloy used is important, too, as well as the thickness and shape. As seen in the video to the left, Vector used an ultra-strong honeycomb layer design for parts of their chassis. A body made out of that would be impractical.
Plastic
Common in trim pieces of most of today's cars, plastic is easy to mold, cheap, and can be made in nearly any color. Plastic isn't particularly strong, but when used on trim pieces, such as mirrors or grille inserts, its low strength isn't much of an issue.
On modern vehicles, a lot of body components which are likely to be hit (such as the front and rear bumpers) are made out of plastic, so they are less costly to replace, and it can sometimes reduce the damage done to the object being hit.
Types of common automotive plastics include ABS (Acrylonitrile-butadiene-styrene), LCP (Liquid crystal polymer), PE (Polyethylene), and VAE (Vinyl acetate-ethylene). All of these are large words for plastics made out of different types of chemicals (some of which are derived from crude oil).
Carbon Fiber
Carbon Fiber is a very strong, lightweight, composite material which is quite appealing in racing conditions and sports cars alike.
Many auto enthusiasts buy a carbon fiber hood and leave it unpainted to show off the fact that their vehicle has one. Rear wings are also a common carbon fiber part. Completely carbon fiber bodied cars are fairly rare, but some high-end cars are made this way. Due to the material's popularity, it may also be found in some interior components like dashboards and gear shifter knobs. Some racing seats and helmets are made partially out of carbon fiber as well.
Fiberglass
Fiberglass is cast in a mold using fiberous glass material (which sometimes look like cloth sheets) and a resin or epoxy, which are plastic or plastic-like materials when dried. The casting process makes mass production relatively inexpensive. As a material, fiberglass is quite strong for its weight, but it can be brittle when bent the wrong way. In racing applications, it is sometimes favored over carbon fiber due to the lower cost to repair or replace it.
Fiber Reinforced Plastic (FRP)
For a short time, fiber reinforced plastic, or FRP, was an appealing strong, lightweight material ideal for use in automotive body manufacturing. This material made it into a number of production cars, but was soon made obsolete when other materials became cheaper to manufacture. This material is sometimes still used, however.