There have been myriad accounts of sea goers and their encounters with creatures unknown to the world. There are reported attacks, harmless sightings, or mysterious carcasses washing ashore.
The descriptions range from giant versions of known species, such as squid or jellyfish, to horned serpents, sea monsters with hair, and anything else imaginable.
Many of the "serpents" are said to swim in an undulating manner, unlike the side-to-side motion of fish. There have also been detailed encounters beasts resembling the thought-to-be-extinct dinosaurs, such as the plesiosaur.
The Kraken of legend is probably what we know today as the giant squid. While a colossal octopus might also fit the description, the squid is thought to be much more aggressive and more likely to come to the surface.
Though giant squids are considerably less then a mile and a half across, they are large enough to wrestle with a sperm whale.