#1 - The White

Although it's called the white, this part of the eye isn't completely white, so it's a good idea to set the basic colour as white, and have your specular colour set to an off-white, as seen in the next image.
You can also see from this image how we've used the 3D Textures - Spots node to give the effect of the tiny blood vessels found in the white of the eye. I've also attached it to the Bump operator for a little more realism.

#2 The Pupil