A small cool faint main sequence star, spectroscopic class M.
Red Dwarfs put out most of their luminosity in the form of infra-red light; for this reason they appear dimmer than G-Class stars when viewed from the habitable zone. However many red dwarfs emit frequnt, bright stellar flares, which are accompanied by bright UV emissions. Any biosphere which exists in the habitable zone of a red dwarf must also tolerate such sudden bursts of UV light.
The habitable zone of most red dwarfs is small compared to other stars, and tidal effects mean that any planet which orbits within this zone will be tidally locked, or rotate in a simple resonance with its own orbital period. Earth-like tidally locked planets of this kind form the Vesperian subclass in the NOLWOCS classification system.
Because they are so cool they only burn slowly, and hence live for a very long time. These are the most common stars; there are about two thousand per million cubic light-years of galactic space. They are located at the bottom right of the Hertzsprung-Russell diagram.
As they get older, red dwarfs increase in luminosity but never become red giants or become white dwarfs. If left unmodified, many red dwarfs will eventually increase in brightness until they become as bright as a sun-like star; for smaller dwarfs, this era will not occur for a trillion years or so. Eventually the oldest dwarfs will cease to shine and become large, helium enriched black dwarfs, slowly radiating their heat and contracting.