Most stellar remnants so far have been found in binary systems, where they interact with matter from their companions. Isolated neutron stars and black holes are difficult to find as they are dark, yet they are predicted to exist in our Galaxy in vast numbers. We explored the OGLE-III data base of 150 million objects observed in years 2001-2009 and found 59 microlensing events exhibiting a parallax effect due to the Earth's motion around the Sun. Combining parallax and brightness measurements from microlensing light curves with expected proper motions in the Milky Way, we identified 13 microlensing events which are consistent with having a white dwarf, neutron star or a black hole lens and we estimated their masses and distances. The most massive of our black hole candidates has 9.3M_{sun}_ and is at a distance of 2.4kpc. The distribution of masses of our candidates indicates a continuum in mass distribution with no mass gap between neutron stars and black holes. We also present predictions on how such events will be observed by the astrometric Gaia mission.