How many Black Holes have been documented to date?
None. Black holes are still theory. We have ideas where some might lurk but we really don’t even know if they exist.
While black holes are still theoretical, no serious astronomer doubts their existance. There are a great many phenomena observed for which there is no other known reasonable explanation. For starters, every galaxy yet observed seems to have a large black hole at the core, and as the Hubble Deep Field shows, there’re a lot of galaxies out there.
Of course, the galactic core holes are only a small fraction of the total number, since there are also many stellar-mass holes (such as Cygnus X-1) in binary systems, which aren’t so easy to detect, and probably a similar number of isolated ones, which would be nearly impossible to detect.
Not too much of a hijack I hope, but since we have Chronos’s attention 
- what is the feeling in the physics community about a recent alternative to the black hole theory, such as gravastars ?
Gravastars have all of the same problems as black holes, plus several of their own. Basically, the folks who came up with the idea don’t know much general relativity (they’re particle physicists, if I recall correctly), and were trying to fix things that weren’t broke.