Big call from the 100% ers there.
A black hole's existance is deduced by observing its effects on the environment and comparing those against effects of known phenomena such as white dwarfs and neutron stars. If the simplest explanation is a black hole then, using Occam's razor, we have a winner.
This is not so much a "proof" as the best explanation we have for a number of observations such as active galaxy's jets and objects such a Cygnus X-1 :
http://spaceflightnow.com/news/n0101/11hubblehole/
and stars behaving badly:
http://www.space.com/scienceastronom...ay_021016.html
This does not preclude other explanations but the case is pretty strong.