The Earth isn't particularly close to any black holes -- the closest candidate, A0620-00, is around 2800 light years away -- so good on us for picking a nice cosmic neighbourhood to live in. But besides the whole "nothing escapes from them" thing and the hugely destructive supernova preceding their birth, black holes are bad news. They could end life as we know it, even from far away. Right after a star collapses into a black hole (or two stars collide to do the same) a tremendous amount of energy is released as a gamma ray burst, Kurzgesagt explains. The ozone layer around Earth generally protects us from the gamma rays given off by our own sun, but a full-blown gamma ray burst is so much more powerful that it would cook the side of our planet that came in contact with it. Gamma rays are also capable of blowing apart the bonds in our DNA. Because these bursts are invisibly and move at the speed of light we probably wouldn't know one was coming until it was too late. One minute the Eastern Hemisphere is going about its business; the next it's a Mad Max wasteland.
The good news is that gamma ray bursts don't happen all that often, and one would have to be coming from within our own galaxy in order to be of serious danger. Between the timescale required, number of black hole candidates nearby, and likeliness of a direct hit, Earth has more pressing things to worry about -- like climate change, a Trump presidency or whether we'll ever see a new season of Attack on Titan.