How many black holes exist? How many black holes exist and what is their distrubtion over mass?
There is a list of black holes, but I'm interested in an estimate of all black holes in the visible universe.
There exists probably about one supermassive black hole per galaxy, hence about 100 billion ($10^{11}$) in the observable universe.

If we take 1% of the stars ending as a black hole as a very rough order of magnitude estimate, we'll get about 1 billion stellar black holes per galaxy, hence about $10^{20}$ stellar black holes in the observable universe, give or take one order of magnitude.

Stars of more than about 15 stellar masses (O class stars) will probably end up as black holes. About 0.00003% of the stars are O-class. The lifespan of a star with 15 solar masses is about 11.5 million years. So, we need to multiply the 0.00003% at least by a factor 1000, since the age of the universe is more than 1000-times the life of an O-class star, resulting in 0.03% of all stars over time should have been O-class stars.
(Most stars are red dwarfs, and have a longer life-span than the current age of the universe.) Star formation, especially of heavy stars, in the early universe has probably been higher than today.
Therefore I'm estimating the number of stellar black holes as about 1% the number of all stars.

Intermediate-mass black holes as presumed centers of globular clusters are harder to estimate, since there isn't much observational evidence. If the hypotheses turns out to be correct, and we take 1000 globular clusters per galaxy, we get about $10^{14}$ IMBHs.

There is no observational evidence for the existence of small black holes (smaller than a few solar masses).