What is a Sea Monster?
Many people have wondered why sea serpents (sometimes also known as sea dragons) have been so well-known throughout history. The biggest thing to note is that the word "monster" is not clearly defined, and thus a "sea monster" is usually anything large and unidentifiable by the person or people looking at it. 
Some have argued that most "sea serpents" were large eels, sea cobras, or ribbonfish (along with other culprits).  Many people don't know what a ribbonfish is, most probably because it is rarely seen alive. It is a fish that has been reported to grow up to fifty feet in length (although there is no evidence of such a length) with a bright red "crest" that sticks up out of its back, giving the appearance of a sea serpent.  In 1860, a "sea serpent" was reported to have washed up on a beach in Burmuda, but it was actually a ribbonfish. 
In addition, the discovery of prehistoric fossils usually reinforced the fact that there were dangerous sea dragons and serpents about.  The major problem with proving whether or not the sea serpents were a different, unknown species is based upon the poor description by the people who saw them.  Sea serpents are said to be large creatures (usually between forty and sixty feet long) with a snakelike head and the tail of a fish, usually with a mane of hair on its head or back. Other descriptions give it a horse's head, a lion's head, and sometimes a turtle's head.
So now brings the question: Where did these creatures come from? It is quite likely that a good deal of them were simply from the imagination or real life creatures that were seen by sailors in poor weather conditions.  Another reason sea 'serpents' were so widespread was that they were linked to dragons. Often, on maps with unchartered water regions, or where several ships disappeared without a trace, the map makers would write "Here be dragons."
To say that there were no sea serpents at all is perhaps too extreme, but to say that every sighting of a sea serpent or sea dragon was true is also too extreme. The fact of the matter is that these sea monsters could very well have been normal marine life, but this does not mean that there are no sea dragons. All it means is that some of these sea dragons were other, classified species.
Impact of the Sea Monsters
Sea monsters casted fear into the hearts of many sailors. When someone was going out on a voyage, they never knew if they would meet up with one of these beasts or not. The Norse believed in them so much that they carved their long ships to resemble fire drakes. 
Mythology was also effected; several dragons are said to hail from the sea at the command of a god, such as Cetus. These great creatures from the sea also effected Celtic Mythology, which tell tales of huge dragons being sent into the sea by saints, such as Paiste. Other dragons, such as Muirdris and Master Stoorworm were said to have also come from the sea.
The Celts, Greeks, Norse, and Romans were not the only ones to believe that serpents and dragons came from the water. Most mythologies tell of dragons that emerge or live in rivers.
Perhaps the biggest impact that still lives on today is the sighting of sea serpents and sea dragons. While many would refer to Nessie, also known as the Loch Ness Monster, there have been other sightings of creatures, such as off the coast of California. 
Olaus Magnus, a Catholic Archbishop, researched this subject in the early to mid-1500s. He wrote a book called History of the People of the Northern Regions which described several sea monsters and even had detailed pictures. These were reproduce over and over again, to the point of where they were even added quite faithfully to encyclopedias. 
The Remains of a Sea Dragon?
Many argue that past dinosaurs that managed to survive to the present day were considered dragons. Indeed, many dinosaurs fit the description of a sea dragon - a large creature with four flippers and a wedge-shaped head. 
In October 2002, a plesiosaur's bones were discovered off the east shore of Yorkshire. Note that these were bones, not fossils. However, this plesiosaur was said to be four metres (about thirteen feet), thereby making it a good deal smaller than most "sea monsters". 
Famous Books About Sea Monsters
Many books have described sea monsters and sea dragons. There are some more recent books, namely those that comment on those listed here, and then there are older books that have become notable. While these books may not have been used for research for this site, they do possess some interesting information for people who desire to read more about sea monsters.
There are older books which present a different image of sea serpents than today's modern view of them; for instance, Olaus Magnus wrote a book that was published in English in 1658 as A Compendious History of the Goths, Swedes, & Vandals, and Other Northern Nations.  His original book was published much earlier, in the early sixteenth century, so it is obvious that the belief in sea monsters would be more finite. This book became the later source for other's encyclopedias, which recounted the stories in Magnus' book. Up until Heuvelmans' book (listed below), the most comprehensive book on Sea Serpents was written in 1892 by Antoon Cornelis Oudemans, who wrote The Great Sea-Serpent. 
Many books look to disprove the theory of sea serpents; for example, in J. R. Norman's A History of Fishes, the author cites many of the sea monsters and serpents to be other creatures of the sea.  On the other hand, there are just as many books that explore the possibility of sea monster existence. Henry Dewhurst's Natural History of the Order Cetacea names several sea serpents (among which was Gloucester's Sea Serpent).  The author Heuvelmans wrote a book called The Wake of the Sea-Serpents, which throws out many theories on their existence; however, it does not fully explore these theories.