What gives milk its characteristic white color?
There is no "pigment" that makes milk white.

According to Wikipedia:


  A pigment is a material that changes the color of reflected or transmitted light as the result of wavelength-selective absorption.


Going by that definition of a "pigment", then there is no (white) pigment in milk. In fact (as @Ivan points out in the comments) there is no such thing as a "white pigment", because that would require the "pigment" to absorb no visible radiation (if it absorbed all visible radiation, it'd appear black)

That's because the real reason for the white color of milk is a physical phenomenon called Scattering. (Source: Optics, 4th edition, E. Hecht)



(Diagram's from Wikipedia)

Milk is an emulsion of fat dispersed as these really tiny droplets in water. These fat globules (and some milk proteins) scatter light of all wavelengths in the visible spectrum. This is why milk appears white

This is the same reason (albeit different cause) as to why clouds often appear white; except here, the scattering is due to suspended water droplets and dust particles.