A pyrotechnic initiator (also initiator or igniter) is a device containing a pyrotechnic composition used primarily to ignite other, more difficult-to-ignite materials, e.g. thermites, gas generators, and solid-fuel rockets. The name is often used also for the compositions themselves.
Pyrotechnic initiators are often controlled electrically (called electro-pyrotechnic initiators), e.g. using a heated bridgewire or a bridge resistor. They are somewhat similar to blasting caps or other detonators, but they differ in that there is no intention to produce a shock wave. An example of such pyrotechnic initiator is an electric match.
The energetic material used, often called pyrogen, is usually a pyrotechnic composition made of a fuel and oxidizer, where the fuel produces a significant amount of hot particles that cause/promote the ignition of the desired material.
Initiator compositions are similar to flash powders, but they differ in burning speed, as explosion is not intended, and have intentionally high production of hot particles. They also tend to be easier to ignite than thermites, with which they also share similarities.
Common oxidizers used are potassium perchlorate and potassium nitrate. Common fuels used are titanium, titanium(II) hydride, zirconium, zirconium hydride, and boron. The size of the fuel particles is determined to produce hot particles with the required burning time.
One of the most common initiators is ZPP, or zirconium - potassium perchlorate - a mixture of metallic zirconium and potassium perchlorate. It is also known as the NASA Standard Initiator. It yields rapid pressure rise, generates little gas, emits hot particles when ignited, is thermally stable, has long shelf life, and is stable under vacuum. It is sensitive to static electricity.
Another common igniter formula is BPN, BKNO3, or boron - potassium nitrate, a mixture of 25% boron and 75% potassium nitrate by weight. It is used e.g. by NASA. It is thermally stable, stable in vacuum, and its burn rate is independent of pressure.
In comparison with black powder, BPN burns significantly hotter and leaves more of solid residues, therefore black powder is favored for multiple-use systems.
Metal hydride-oxidizer mixtures replace the metal with its corresponding hydride. They are generally safer to handle than the corresponding metal-oxidizer compositions. During burning they also release hydrogen, which can act as a secondary fuel. Zirconium hydride, titanium hydride, and boron hydride are commonly used.
THPP (titanium hydride potassium perchlorate) is a mixture of titanium(II) hydride and potassium perchlorate. It is similar to ZHPP. Like ZHPP, it is safer to handle than titanium-potassium perchlorate. 
Formation of an intermetallic compound can be a strongly exothermic reaction, usable as an initiator.
Titanium-boron composition is one of the hottest pyrotechnic reactions in common usage. It is solid-state, gasless. It can be used as a pyrotechnic initiator or for heating confined gas to perform mechanical work. 
Palladium-clad aluminium wires can be used as a fuse wire, known as Pyrofuze.  The reaction is initiated by heat, typically supplied by electric current pulse. The reaction begins at 600 °C, the melting point of aluminium, and proceeds violently to temperature of 2200-2800 °C. The reaction does not need presence of oxygen, and the wire is consumed. 
Pyrofuze comes as a solid wire of different diameters (from 0.002" to 0.02"), braided wire, ribbon, foil, and granules. Palladium, platinum, or palladium alloyed with 5% ruthenium can be used together with aluminium.  Pyrofuze bridgewires can be used in squibs and electric matches. Pyrofuze foils can be used for e.g. sealing of various dispensers or fire extinguishing systems.  Palladium-magnesium composition can also be used, but is not commercially available or not at least as common. 
BNCP, (cis-bis-(5-nitrotetrazolato)tetraminecobalt(III) perchlorate) is another common initiator material. It is relatively insensitive. It undergoes deflagration to detonation transition in a relatively short distance, allowing its use in detonators. Its burning byproducts are of relatively little harm to environment.  It can be ignited by a laser diode.
Lead azide (Pb(N3)2, or PbN6) is occasionally used in pyrotechnic initiators.