Although some people have blue eyes, and many babies are born with particularly deep blue irises, no one actually has blue pigment in their irises. They're just a trick of the light.
With the news of Elizabeth Taylor's death, many people's thoughts have turned to eye color. It's known that her famous violet eyes were mostly the result of make-up and photo coloration, but even outside of the world of starlets many people rhapsodize about blue eyes. This is especially true with parents, who are startled by the deep blue of their babies' eyes. When people say that their children's eyes are sky blue, they're telling the truth. Blue eyes are blue for the same reason the sky is blue - scattered light.
Irises are made up of three layers, a thin top and back layer, with a spongy layer in between called the stroma. Any layer can have pigmentation in it. There are a few different colors of pigment that come into play. Most people have either dark brown or yellow pigment in at least one of these layers. The combination of yellow and brown go into making brown and amber-colored eyes. Brown-eyed people have these pigments are in each layer of the iris, giving the eye a strong brown color.
Blue and grey eyes, on the other hand, only have dark brown pigment on the back layer of the eye. The stroma has no pigment, but it does have small particles suspended in it. These particles give rise to the Tyndall Effect. The small particles in the eye scatter blue light. As light enters the eye, the blue wavelengths are scattered - some of them back towards the outside of the eye. The dark background absorbs most of the rest of light. (If the background of the eye were white, or were lit from within, more light would stream through, the blue wavelengths would be scattered out, and the eyes would look yellow.) Babies can often have blue eyes for a few days or months after birth, because the melanin - the darkening pigment of the eyes - has not fully developed in the stroma.
Even if the overall color of the eye doesn't change, babies and young children tend to have more intensely blue eyes than adults. As people age, the particles in the stroma get bigger, and scatter white light. Add a layer of white is added to the blue, it comes to look more grey. People can see this kind of pigmentation in weather. A dry sky is made up of tiny particles that scatter blue light and make the sky look blue. As clouds start to form water molecules fill the air, and the color of the sky changes to a whitish grey.