The five most common horse coat colors are chestnut, bay, black, grey, and pinto.
Chestnut- also called sorrel- is a basic color featuring brown, ranging from pale (flaxen chestnut) to reddish to deep dark brown (liver chestnut). Bay horses are brown with black mane, tail, and "points" Black Horses may be true black looking, or may appear to fade to reddish-brown in summer.
Grey horses may be born any color, the grey gene is a modifier that changes whatever color the horse genetically is.
Pinto horses are multi colored, usuall brown and white or black and white. Do not confuse pinto with Paint. Paint horses are a breed of horse with pinto coloring. Pinto is a term describing markings-only that can be used to describe pinto colored horses of any breed.
These most common horse colors can be found in almost any breed. The first four coat colors listed can be found in all breeds that are not color-based. (For example, clevland bays do not allow chestnuts, Friesians will not register greys or bays, etc) But pinto horses are not accepted in multiple registries (and thus, have their own color based registry).