Yes, they do—Stephen Hawking discovered that according to quantum mechanics, black holes should radiate energy. In the quantum world, space is filled with tiny particles that flash in and out of existence, and Hawking predicted that energy fluctuations would generate particle-antiparticles near a black hole’s event horizon. Before they can annihilate each other as would normally happen, the black hole pulls in the particle with negative energy and “emits” the particle with positive energy. For this reason, black holes aren’t completely black—they glow faintly.
This is called Hawking Radiation, and it results in the black hole losing energy and therefore mass according to E=mc^2. As a black hole radiates, it shrinks. The nature of the radiative process means that the more a black hole shrinks, the more it radiates—so eventually the black hole will disappear. This will take an incredibly long time, though. A black hole of the mass of the Sun will take a billion times a billion times a billion times a billion times a billion times a billion times the age of the universe to evaporate completely.