Typically used as rocket propellants, hypergolics are fuels and oxidisers that spontaneously and reliably ignite when they come in contact with each other.
Also known as hypogolic. Editor's note: 'hypogolic' is a common typo; I do not believe that it is ever properly used as a technical term.
Hypergolics are used in some forms of rocket engine construction because of their simplicity and controllability (unlike the metal base fuel used in solid rocket boosters). Hypergolic fuel engines require separate storage tanks, some type of mixing control, and a combustion chamber (and the requisite nozzle). Notable by its absence is an ignition system, which greatly reduces the complexity of the engine.
Hypergolic fuels are most well-known by their use in the U.S.A. space shuttle. The shuttle's Orbital Maneuvering Subsystem (OMS) and Reaction Control System (RCS) both use hypergolic fuel engines. The fuel component is monomethyl hydrazine (MMH) while the oxidiser is nitrogen tetroxide (N2O4). The ease of storage of these two chemicals is counterbalanced by their extreme toxicity and the extreme safety requirements needed to handle them.
Hypergolic fuels were also used in the Messerschmitt Me 163 Komet.
Hydrocarbons mixed with LOX (liquid O2, not the fish) are not hypergolic, because they require some (small) nudge or spark to (violently) react. They can be made hypergolic when the LOX has a substantial percentage of fluorine added.