All stars eventually end up dying. The nature of the corpse depends on the mass of the star...some collapse into white dwarfs, others neutron stars, and the most massive collapse entirely into black holes.
Smaller stars, less than 1.4 of our suns, become white dwarfs,
larger ones, up to 2 or 3 of our suns end up as neutron stars,
bigger than that: black hole!
In a neutron star, there is enough gravity (enough mass) to crush electrons into the nucleus, so electrons and protons become neutrons, hence the name, but there is not enough gravity to further crush the particles out of existence and form a black hole.
A http://en.wikipedia.org/wiki/Neutron_star" [Broken] is a highly dense objects that form from a collapsing star. They are so dense that a single teaspoon of neutron star matter could mass around 2.5 billion tonnes!
A http://en.wikipedia.org/wiki/Black_hole" [Broken].
Depends mainly on the progenitor star mass. Progenitor stars up to ~10.5 solar mass will become white dwarfs. From 10.5 ~20 solar masses, a neutron star is the usual result - for isolated stars. In binary star systems, a neutron star may result from progenitor stars of 50 or more solar masses [re: http://arxiv.org/abs/0804.4143] [Broken]. The Chandrasekhar limit applies to the mass of the remnant star and is actually rather uncertain if you fully account for relativistic and centrifugal effects.
Smaller stars, less than 1.4 of our suns, become white dwarfs,
larger ones, up to 2 or 3 of our suns end up as neutron stars,
bigger than that: black hole!
but instead:
Smaller stars, less than about 8 of our suns,
larger ones, from about 8 to 20 solar mass, end up as neutron stars,
bigger than that: black hole.
Source: BLACK HOLES AND TIMES WARPS, Kip Thorne, pg 206
"The preponderance of the observational data suggest (but do yet firmly prove) that most stars born heavier than about 20 suns remain so heavy when they die that their pressure proivdes no protection against gravity..." He's referring to that fact that stars may blow off mass/energy as in supernovas.)