(Eve) From the Science of Cooking Web site

The greenish hue is actually chlorophyll, but it is also an indicator that an alkaloid, called solanine, may be present under the skin of the potato. Solanine develops in potatoes when they are stored in the presence of light (which also encourages chlorophyll formation) and either at very cold or quite warm temperatures. It is toxic, however it would take a very large number of green potatoes to make you ill.
Since solanine collects just under the skin, it is safe to peel away the skin and a thin layer of white flesh before you cook the potato. The sprouts, too, can be toxic and shouldn’t be eaten, though it would take many sprouts to make you ill. (Sir Oliver: Green potatoes don’t taste pleasant and have less starch content, making for a very boring spud.)

It’s best to check potatoes for any green coloring before you buy them. Then, store them at cool room temperature in a dark, dry place.