Copper has historically been the most common type of pipe used in home plumbing. Due to its reliability and durability, it became very popular in the 1960s and quickly became the standard material. Copper is resistant to high temperatures and corrosion, but it may split if water freezes in the pipe in very cold weather. Copper is more expensive than most other types of piping, and will sometimes be stolen from building sites during construction for sale to scrap metal dealers.
Galvanized steel was used in homes prior to the 1960's and the widespread adoption of copper, but it can still be found used in some older homes. Galvanized pipes were especially popular in carrying water into the home from wells, and waste-water out to sewers. The gray galvanized coating helps prevent rust, but the interior of the pipes were prone to leaking, corrosion and sediment build-up that reduces the overall flow of water. These were all factors in the gradual diminishing use of galvanized steel and increased use of copper.
Stainless steel is not a common type of plumbing pipe, and as such it is hard to find and rarely seen in use in homes today. It is an expensive material for piping, especially since copper is a much more appropriate choice. One beneficial characteristic is that stainless steel is better able to withstand the corrosive nature of salt water over other pipes, and it is often used in marine environments for that reason.
PVC, or polyvinyl chloride, is a form of plastic pipe used for plumbing high-pressure water. PVC is most commonly used for drains, and is usually white or gray in color. It's less expensive than copper, but will similarly split in cold weather. It's only capable of handling cold water transfer because hot water will warp PVC pipe, so it needs to be used in addition to another type of pipe for hot water.
Although available since the 1920's, PEX has only become popular recently due to ease of use and lack of leaks. PEX, a form of polyethylene pipe is considerably less expensive than copper, but has an equal diameter and is capable of handling both cold and hot water. It is highly flexible tubing, and requires very few joints that would make it more prone to leaking. It comes in both red and blue colors to easily denote water line temperatures on sight. A downside is that it can look unprofessional or cheap when compared to the usual copper pipe.