The most common type is steel. Steel horseshoes are readily available and easiest to use. They can be easily modified or forged from barstock with only minimal forging skills. Steel is easily welded or brazed for specialty applications. Steel comes in a variety of widths, thickness and configurations.
Many farriers die of old age without ever nailing on anything but steel shoes.
Occasionally though, horses need other kinds of shoes. Aluminum is also very popular on the fronts of hunters as many trainers feel it enhances a hunter's way of going. Aluminum is not quite as easy to forge or weld as steel. Titanium is sometimes used on horses that need a light, very strong shoe in front. Titanium is easily forged or swedged into specialty configurations, but must be TIG welded.