Angora goats come in three main color classifications: white, black and brown (also called "red").
White is just that. White goats are the majority of the world's angora population, and have been bred for fineness of fiber and complete white coverage for centuries. However, white goats that show color in their horns, flesh or hooves are color-carriers, and, with the right breeding, could produce kids with colored fleeces. I own one white goat and one black goat that just happens to have a white fleece. (Go figure.)
Blacks include goats with fleeces that range from a deep solid black to light grays and silvers. They also come in a variety of patterns. The most common patterns are: solid; reverse badgerface; white/tan stripes through the eyes; and white/tan chin and belly on a silver to black goat.
Reds are often called "faded reds" because the color of the fleece lightens significantly as the goat ages. Fortunately the color does not fade away completely from all red goats. The fleeces range from apricot to copper. Red goats are generally solid color. Color patterns include the combinations mentioned previously.
Go to the CAGBA patterns page for drawings and pictures of the named/categorized patterns.
Go to the Hill Shepherd photo album for some fantastic colors as well as white goats.