Lists of astronomical sources are called "catalogues" and other answers have already mentioned the NGC catalogue of galaxies and nebulae. However, you asked about quasars and black hole x-ray binaries.
I say "sources" because the catalogues normally list what can be observed, rather than what can be inferred. For black holes, this is significant, as we can rarely observe black holes directly, but we can infer their existence from the effects that they have on other matter.
For quasars, there are several catalogues. None claim to be complete, as new discoveries happen all the time. The MILLIQUAS catalogue is a compendium of 460,222 type-I QSOs and AGN. It also contains about a million "Quasar candidates". (sources that may be quasars, 80% confidence)
For Black hole binaries, the difficulty is proving that the object is indeed a black hole. This usually requires calculating the mass of the accreting object, which is not always easy. The X-ray catalogues are classified by the mass of the normal stellar component. The High Mass x-ray binary catalogue notes objects that are "black hole candidates". It is in no way a definitive list, since no such list exists.