For most of their lives, stars exist in a state of equilibrium between gravity, which pulls the star's mass inward, and radiation pressure, which pushes outward. Eventually, the nuclear fusion in a star's core stops; the radiation pressure decreases and gravity takes over. For stars smaller than about 1.4 solar masses (the Chandrasekhar limit), gravitational collapse results in a white dwarf. Stars with masses from 1.4 to something over 3 times that of the sun (the Tolman-Oppenheimer-Volkoff limit, which is not yet as well understood as the Chandrasekhar limit) collapse into neutron stars. The collapse of more massive stars results in black holes; the smallest known black hole has an estimated mass 3.8 times that of the sun.

Note, however, that these masses are for the star (or remnant thereof) at the time of its collapse. Stars lose significant amounts of mass as they age, and supernova collapses involve only the star's core (the rest of the star is blasted into space), so the original main-sequence stars are more massive than their final stages might suggest. A main-sequence star of less than about 8 solar masses will end up as a white dwarf, a star of between 8 and 20 solar masses will become a neutron star, and a main-sequence star with a mass greater than about 20 suns will eventually form a black hole.

The origin of the supermassive black holes found at the cores of galaxies is still unclear. They may form through accretion of matter by stellar black holes, or by the spontaneous collapse of unstable "relativistic stars," or possibly as a result of the sheer mass accumulating at the core of a galaxy. The physical size of a black hole (its Schwarzschild radius) is proportional to its mass, so the volume of a black hole increases as the cube of its mass. This means that supermassive black holes can be less dense than water or even air, so the matter making up a supermassive black hole does not need to be compressed as much as for a stellar-mass black hole, possibly making it easier for the necessary mass to accumulate.
Source(s):
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/010607a.html
http://en.wikipedia.org/wiki/Black_hole#Gravitational_collapse
http://www.nasa.gov/centers/goddard/news/topstory/2008/smallest_blackhole.h...
http://imagine.gsfc.nasa.gov/docs/science/know_l1/dwarfs.html
http://en.wikipedia.org/wiki/Supermassive_black_hole#Formation
http://library.thinkquest.org/25715/formation/supermassive.htm

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