Black holes exist

It may come as a surprise to lay readers to learn that even as recently as 10 years ago there were prominent physicists who still doubted the existence of black holes.

For example, there's Sir John Maddox, a trained chemist and physicist who was editor of Nature for 22 years. In a book published in 1998 (What Remains to be Discovered), he wrote, "The concept of black holes raises serious difficulties of a philosophical character." (p. 43) (Remember what C. F. Gauss said about philosophers.) And, "The habit of others in referring to black holes as "putative" seems to imply a collective uneasiness about the concept." (p. 112)

But recent skeptics of black holes are in good company. Einstein, for one, vigorously objected to the idea. Around 1935 Subrahmanyan Chandrasekhar, later a Nobel Prize winner and now celebrated, but only in his mid-20s at the time, had the audacity to argue that black holes might form from collapsed stars only 1.44 times as heavy as the Sun – and nearly had his career wrecked from Sir Arthur Eddington's sharp criticism.

Even very recently one still sees theoretical studies that offer alternatives to the standard relativisic model of black holes.

Nevertheless, to the consternation of skeptics, the evidence for the correctness of the standard model of black holes just continues to pile up:
Quasar tests general relativity to the limit

                                                        [T]eam leader Mauri Valtonen of Tuorla Observatory in Finland claims the work provides the first hard evidence for black holes, which are so massive that space–time is predicted to completely curve in on itself: "People refer to the concept of black holes all the time, but strictly speaking one first has to prove that general relativity holds in strong gravitational fields before we can be sure that black holes exist," he told physicsworld.com.

And actually, the more significant part of that research is its validation of general relativity in very strong gravitational fields:

Astronomers have obtained the most compelling evidence yet that massive objects dramatically warp space–time, as predicted by Einstein's general theory of relativity. Although the geometric nature of gravity was first demonstrated in 1919, when Arthur Eddington famously detected the subtle warping effect of the Sun on the light from distant stars, the new results provide the first test of Einstein's theory in much stronger gravitational fields.