How many colors are there? A lot, as this atlas by Tauba Aurebach illustrates:

american artist tauba auerbach presents the 8 x 8 x 8-inch hard-back cubes illustrating the RGB color scheme in a page-by-page medium. a digital offset print on paper with airbrushed cloth cover and book edges create a colorful reference volume of all the colors in existence. 

Link -via Nerdcore | Artist's Website