A house can be topped with a variety of roofing materials, each with distinct advantages and disadvantages. Location is a main concern when selecting materials, for example in coastal areas where hurricanes are common a sturdier material is used. In the medical profession a popular phrase is "doctor heal thyself," but in the world of homes it's "owner know thy roof."
A base of glass fibers covered with ceramic coated granules are fiberglass asphalt shingles . This is an inorganic shingle with a high fire rating and often a longer warranty (and life span) than other types of shingles. This type of shingle does not absorb water, and it resists cracking. According to Underwriter Laboratories it can also withstand high winds. Seems like a winner!
An inorganic, three dimensional shingle is Architectural Shingle. Because it is multi-layered it has depth and thus an appearance closer to wood or slate roofing. These shingles weigh more and cost more than most other shingles.
Roll roofing is less expensive than shingles. It can be used with shallow grades, or on steeper roofs as a compliment to shingles. This is used most often on industrial buildings. It consists of a heavy felt base, saturated with asphalt, covered by a smooth or mineral surface. Easy to install, this type of material will last between 10 and 20 years.
Metal roofing is steel panels used in place of shingles. Zinc is used in the best steel panels. Like roll roofing this is more common on industrial buildings. It is durable, withstands fire, and lasts a long time.
The earliest shingles were made of wood, and wood shingles are still used in modern construction. Cedar is the most common wood used for these shingles, but many consist of a variety of woods. These are more difficult to install than asphalt shingles. Wood burns. A fire-retardant coating reduces the flammability, but cannot eliminate it.
In the interest of being complete, a discussion of other elements is necessary. These are not shingles or tiles or total roof coverings, but nevertheless are important elements. Flashing consists of material or sheet metal strips used to cover joints, to make the joints waterproof. The boot is a flashing made to fit around the base of a vent pipe. Boots containing lead generally last longer. A Drip Edge is an "L" shaped, weather-resistant material placed at exposed roof edges to shed water and protect the wood parts. Felt paper, or building paper, is a sheet with a tough, fibrous base saturated with asphalt installed under shingles. Building paper helps keep water away from the wood frame under the shingles.
A great source of information on roofing materials is the Internet. The more you know the less likely you are to get wet.