A number of fish can glow. Some glow under normal light -- and would also appear bright under a black light. Others have the ability to fluoresce under ultraviolet light thanks to genetic engineering. Several mechanisms allow such fish to glow under black lights.
Many marine fish glow in the dark. Such fish would glow under a black light. However, almost all marine fish who glow in the dark do not do so on their own. Instead, their bodies harbor a bacteria that can glow in the dark -- or under black lights. Deep sea fish such as the anglerfish and the flashlight fish have a symbiotic relationship with these bacteria, allowing the bacteria to grow inside their bodies, producing a glow. The flashlight fish can actually "turn off' by shifting organs to hide the glow.
Researchers recently discovered a fish who can glow under a black light without any bacterial help. The Japaneses freshwater eel (Anguilla japonica) produces a protein that fluoresces under black light. If you've ever had sushi, you may know this eel as Unagi. It is the first vertebrate known to glow like this without genetic engineering or a glowing symbiote. Oddly, the protein that glows functions just as well under low oxygen conditions, unusual for such a protein.
GloFish are fish genetically engineered to glow under black light. Right now, glowing zebra fish are the only commercially available genetically engineered fish, but researchers are working on adding the glowing gene to various cichlids, including freshwater angelfish. As an odd side note, their creator, Dr. Richard Crockett owns a patent on GloFish, making it illegal to sell them without paying royalties.
Glowing has different purposes for different fish. In the freshwater eel, it appears that the ability to fluoresce under black lights is incidental, a side effect of other biological processes. GloFish were produced to test genetic engineering techniques, detect pollution and possibly illustrate tumor growth for research purposes. Marine fish who glow use this ability to attract food and mates, or sometimes as a form of active camouflage called counter-illumination. In this form of camouflage, flashlight fish shine light from their stomachs to match the illumination coming from the water's surface, making them almost invisible to predators below them.