And now, Part 2. If you eschew the chemical dyes and wish to channel your inner Laura Ingalls Wilder, this post is for you.
When I was little, I used to watch my grandmother dye eggs according to the Onion Skin method, which produces eggs like those shown below. Instructions are here.
You can also create stunning red eggs, in the Greek tradition.
Lastly, Martha Stewart has (of course!) a very comprehensive guide detailing many different types of dying methods and their resulting colors. Beets, cabbage, and coffee - oh my!