What are Hypergolic Rocket Fuels? (Other than Explosive, Corrosive, Toxic, Carcinogenic and Orange)

Hypergolic fuels are a core technology in rocket science, propellents that will spontaneously combust when mixed together. This makes them attractive for rocket designers, who generally aren't the people who have to get in a the protective gear to load the stuff.
So, what are they made of, and why do designers pick one option over another?