Many sources list sailfish as the fastest fish in the ocean. These fish are definitely fast leapers, and are likely one of the fastest fish at swimming short distances. This site describes speed trials in which a sailfish was clocked at a speed of 68 mph while leaping.
Sailfish can grow to about 10 feet long. These slim fish can weigh up to about 128 pounds. Their most noticeable characteristics are their large first dorsal fin (which resembles a sail) and their upper jaw, which is long and spear-like. Sailfish have blue-gray backs and white undersides.
Swordfish are a popular seafood and another fast-leaping species, although their speed is not well-known. A calculation supposedly determined that they could swim at 60 mph, and this article claims speeds of 130 kilometers per hour, which is about 80 mph.
The swordfish has a long, sword-like bill, which it uses to spear or slash its prey. They have a tall dorsal fin and brownish-black backs with a light underside.
Swordfish are found in the Atlantic, Pacific and Indian Oceans and in the Mediterranean Sea. These may be the most famous fish on this list due to the story of The Perfect Storm, about a swordfishing boat from Gloucester, MA that was lost at sea during a storm in 1991. The story was written up into a book by Sebastian Junger and later became a movie.
Marlin species include the Atlantic blue marlin (Makaira nigricans), black marlin (Makaira indica, Indo-Pacific blue marlin (Makaira mazara), striped marlin (Tetrapturus audax) and white marlin (Tetrapturus albidus. These fish can be easily-recognized by their long, spear-like upper jaw and tall first dorsal fin.
This BBC Video says that the black marlin is the fastest fish on the planet. This information is based on marlin caught on a fishing line - the marlin is said to be able to strip line off a reel at a rate of 120 feet per second, which would mean the fish is swimming 80 miles per hour. This page lists the marlin (genus) as capable of leaping at 50 mph.
The wahoo (Acanthocybium solandri) lives in tropical and subtropical waters in the Atlantic, Pacific and Indian Oceans and the Caribbean and Mediterranean Seas. These slender fish have a bluish green back, and light sides and belly. Wahoo grow to a maximum length of about 8 feet, but they are more commonly about 5 feet long.
The wahoo's maximum speed is said to be around 48 mph. This was confirmed by scientists that studied a wahoo's speed (see this article), measured a wahoo's bursts of swimming speed, results varied from 27-48 mph.
Both yellowfin and bluefin tuna are said to be extremely fast swimmers, and it appears that while they usually cruise slowly through the ocean, they can have bursts of speed over 40 mph. In a study (also cited above) that measured swimming speeds for wahoo and yellowfin tuna, a yellowfin's burst of speed was measured at just over 46 mph. This site lists the maximum speed of an Atlantic bluefin tuna (leaping) at 43.4 mph.
Bluefin tuna can reach lengths in excess of 10 feet. Atlantic bluefin are found in the western Atlantic found from Newfoundland, Canada, to the Gulf of Mexico, and in the eastern Atlantic, throughout the Mediterranean Sea and from Iceland down to the Canary Islands. Southern bluefin are found throughout the oceans in the southern hemisphere, in latitudes between 30 and 50 degrees.
Yellowfin tuna are found in tropical and subtropical waters worldwide. These tuna can grow to over 7 feet in length.
Albacore tuna are also capable of speeds up to about 40 mph. Albacore tuna are found in the Atlantic Ocean, Pacific Ocean and Mediterranean Sea, and are commonly sold as canned tuna. Their maximum size is about 4 feet and 88 pounds.
Bonito, a common name for fish in the genus Sarda, includes several species of fish (such as the Atlantic bonito, striped bonito and Pacific bonito) that are in the mackerel family. Bonito are said to be capable of speeds of about 40 mph when leaping.
Bonito grow to about 30-40 inches, and are a streamlined fish with striped sides.