The dorsal fin gives the goldfish stability in the tank.
Some goldfish have longer dorsal fins than other goldfish, while some goldfish have no dorsal fin at all. Another difference between the dorsal fin in goldfish can be the height. From Lionheads and Ranchus, that have no dorsal fin, to the veiltail variety of goldfish that can have a long dorsal fin. Goldfish with an average size dorsal fin a sign of good health is an upright dorsal fin, while the longer dorsal finned varieties of goldifsh it is regular to have a bend in the dorsal fin.