As with the other major cryptids (bigfoot, yeti, Loch Ness Monster), it would be impossible to provide an entire history of sea serpents; I have given an overview of the sea serpent's history, and some of the more important (or interesting sightings).
The name "sea serpent" has often been given to almost any strange creature seen in the ocean, as long as it appears to be only slightly serpentine. The first sighting listed in Heuvelman's book, In the Wake of the Sea Serpents, dates from prior to 1639, though sea serpents were almost certainly seen long before then. Some older soures refer to similar creatures, though Medieval and earlier sightings loose some of their credibility when we consider some of the other things people reported seeing (dragons, mermaids, etc).
Olaus Magnus, in 1555, described sea serpents that were supposedly 200 feet long and 20 feet wide, along with other unbelievable details. A sea serpent (probably a Super-Otter) was seen in 1734 by Hans Egede. Another well known sighting occued in Gloucester, Massachusetts, in 1817. Many people reported seeing a 45-50 foot sea serpent near the harbor, after which several people gave sworn testimonies about the serpent. Later, a baby sea serpent was believed to have been killed near the area; unfortunately it turned out to be a blacksnake.
Probably the most famous sea serpent sighting ever was seen in 1848 by the crew of the Daedalus. According to the captain, Peter M'Quhae, a large sea serpent had swam by their ship, which was confirmed by the ship's crew.
Supposedly part of the head and neck came out of the stomach of a sperm whale killed by whalers in 1937. Unfortunately, someone had the brilliant idea to toss the remains into the ocean, and conviently loose any actual evidence.
There have been several incidents where something that looked like a sea serpent was washed on shore, which turned out to be nothing more then a basking shark. Because of the way Basking Sharks rot, the lower jaw and other parts of the body often fall off, making the remaining parts of the corpse look similar to a Plesiosaur.
In 1962, Edward Brian McCleary reported a run-in with a carnivorous sea serpent. He and four other companions had been stuck on a raft after diving near Florida, when they saw some kind of sea creature. They pannicked and tried to swim for it. As they tried to swim away, he reported hearing 3 of his companions screaming as they were killed by the monster (as he didn't see them die, they could have been killed by something else, though). He then saw the creature surface and dive ontop of his remaining companion. Somehow he managed to reach the safety of the shore. Wheter or not his story about the sea serpent is true, the four divers with him did die, either from drowning or from some other cause. Three of the bodies were never recovered; one of them later washed ashore.
In 1964, one looks like a clear photograph of a sea serpent was taken by Robert Le Serrec, off of Hook Island. It seemed to have some sort of wound in it's tail. According to Serrec's story, they were afraid to arrouse the creature in case it destroyed the boat. For some reason, he wasn't afraid to dive in and try to film the creature; the film that he took has never surfaced. Another thing that weakens Le Serrec's credibility (along with the fact that he was already wanted by Interpol) is that in 1959, he is reported to have tried to get some people to come with him, saying that he had something to do with a sea serpent that would get them a lot of money. It is still uncertain as to wheter or not the photo is a hoax.
In 1977 it appeared that the Japanese ship, the Zuiyo Maru had accidentally caught a decaying carcass in it's nets at 900 feet. The corpse seemed to have some resemblance to a plesiosaur or other prehistoric marine reptile. Some photos and samples were taken of the carcass before it was tossed overboard due to it's horrible stench. Later, the samples taken proved that it was another basking shark corpse.
There still remains the question of just what is the sea serpent. One theory is that the Oarfish, an eel-shaped deep water fish that is known to grow to at least 25 feet, is responsible for sea serpent sightings. The problem with this is that, being a deep water fish, the Oarfish would rarely be seen at the surface. There is also the theory that a giant squid, swimming with it's tentacles sticking into the air could be mistaken for a sea serpent. However, the Giant Squid is also a deep sea animal, and is rarely seen at the surface. Others have suggested that they are surviving marine reptiles from the Age of Dinosaurs. Another possible explanation would be surviving Zeuglodons, a species of prehistoric whale that had a somewhat serpentine shape. Bernard Heuvelmans proposed several different species, as many of the sea serpent sightings seem to describe very different animals (for more information, see Types of Sea Serpents).