Pendulous ears - Long lop ears (also called 'lop ears'), having nearly a bell shape - going out in the middle and coming in to a smaller curve on the bottom. Found in the USA on the Boer and Nubian goat breeds.
Erect ears - Shorter ears, oval in shape coming to a point and standing 'up' on the goats head. Found in most dairy breeds - Saanens, Alpines, Oberhasli, Toggenburg, Nigerian dwarf, and also in the meat breed pygmies.
Airplane ears - much like Erect ears only slightly longer and standing strait out or down from the goats head instead of going up. Can be found in any of the erect ear breeds, or also in cross breed between a pendulous and erect eared breeds.
Kinked ears can also be found in cross breeds of lop and erect ear breeds - Typically the ears start to go out like airplane ears and then fall down in at the middle into a short lop ear.
Elf or Gopher ears - Having nearly no outer ear - found in the Lamancha breed. The distinction between the two is in how long the outer ear is - a straight out (just cartilage) or under 1" is a Gopher ear and more desirable for the Lamancha breed. Elf ears come out enough that there is actually a flap of flesh - the ear will either bend up or down, and can be no longer then 2" to qualify for registration (ADGA).
There may be other types of ears, but these are the most common in dairy breeds for the USA.