What kinds of artificial valves are there?

The two main types of valves are "Mechanical" and "Bioprosthetic". Mechanical valves have simply been devised from scratch, and are made of metal or similar materials. Bioprosthetic valves are fashioned from animal or human tissues.

Mechanical valves. There are several different varieties, including "bileaflet tilting valves" which are extremely popular and reliable. Tilting single disc devices are also quite popular. Older models included the "caged-ball" device and "floating discs". The body does not recognize these as "foreign", and thus there is not a fear of rejection. Mechanical valves are generally felt to have the advantage of lasting the longest time. Their main disadvantage compared to other types of valves is the need to take potent blood thinners which decreases the tendency to form clots on their surface.

Bioprosthetic valves. These use some biologic material in their composition. They are all treated, and do not carry the risk of rejection. Treated aortic valves from human cadavers, treated pig aortic valves, and valves fashioned from the pericardium (the outside lining of the heart) of cows are all utilized. These types of valves do not necessarily require that the patient take blood-thinners, but generally do not last as long.
Please note that there are pictures of various valves below.