The norse kings had an organised system for assembling a navy (the "Leidang") when necessary. The ships used for this purpose were usually sea going longships with 20 - 25 pairs of oars. They were fast sailing ships with loading capabilities only for the crew itself. Several descriptions of battles at sea indicates that greater ships than these were slower and heavier to manouver with oars.

Still, many kings and chieftains wanted larger ships because their higher gunwhale and stems made them difficult to attack during sea battles. They where also symbols demonstrating the kings status and superiority. The largest ships were given names and are sometimes mentioned in contemporary poetry and in historical sagas.
These ships were longships, but they were subdivided into serveral different classes like "snekke", "skeide", "busse" and "drake". The differences between them is lost in time, but might have had something to do with the number of strakes above the waterline, raised platforms in the stem and so on.

"Drake" means dragon in english. These ships were equipped with carved dragonheads on top of the stem, while the stern often was shaped like a dragons tail. Many websites in english refer to these ships as "drakkars", which in my opinion unfortunately gives less meaning than calling them "dragons". But the term drakkar seem to be well established as a term referring to a longship with a dragon head.
Please understand that not all viking longships were equipped with a dragon head. So a specific longship was not necessarily a dragon ship (drakkar), unless it had a figure head on top of the stem. As a consequence most longships were not dragon ships! Read more about the different viking ship categories here >>.

These are some of the famous ships menitioned by their names in the norse sagas:

"Trana" - ca 995 AD

A ship built for king Olav Tryggvason of Norway (973 - 1000 AD). It was built at Nidaros, Trondheim, Norway. It was a longship of the "snekke"-type with 30 "rooms"/ 30 seats for the oarsmen and tall stem and stern.

"Ormen Skamme" - a.k.a. "Ormen Korte" - ca 990 AD

Longship of dragon-class built in the end of the 10th century for the chieftain Raud den ramme, Salten, Hålogaland, northern Norway. It had 30 "rooms"/pairs of oars, and was large in relation to this number of oars. It was decorated with golden dragonheads. Its length was probably about 32 - 34 m.
The ship was later captured by the king of Norway Olav Tryggvason and Raud was killed. Olav Tryggvason was very pleased with this ship and it became a model for the more famous ship "Ormen Lange". When the latter ship was finished the first ship was renamed "Ormen Korte", which translates into "The short Dragon"/"The short Serpent".
In norwegian translations of Heimskringla by Snorri Sturluson the ship is named "Ormen Korte", "Ormen Stutte" and "Ormen hinn skamme" (old norse/icelandic).

"Ormen Lange" - ca 996 AD

This ship was built for the norwegian king Olav Tryggvason in the end of the 10th century AD at Ladehammaren in Trondheim, Norway. It became legendary for its size and extraordinary finish already when it was in use and later in the sagas about Olav Tryggvason. It was a "busse" with 34 "rooms"/seats for 68 oarsmen. Its length may have been as large as 40 - 42 m, and the width 6 - 7 m. In the stem it had a golden dragonhead and a golden dragontail at the stern, making the hull form a dragonlike shape. "Orm" means dragon or large snake. In old norse its name was "Orm hinn langi", which simply means "The long Serpent". The gunwhale "was as high as on ocean ships" according to Snorre Sturlason, thus the hight from keel to gunwhale was perhaps as large as 4 m. My guess is that the gunwhale was made extra high to make the ship more difficult to attack from lower ships. Close to the stern its floor was raised to give its crew additional advantage in close combat. One of the shipbuilders is mentioned by name in the saga - Torberg Skavhogg.

In the year 1000 AD all these three ships took part in the famous sea Battle at Svolder, commonly believed to be close to todays Rügen in Germany. In this bloodshed king Olav Tryggvason was defeated and killed by a party of the dane king Svein, the svea king Olav and earl Eirik Håkonsson from Norway. After the battle the "Ormen Lange" was taken by earl Eirik.
A new theory is that this Battle actually took place at Svinesund, between todays Norway and Sweden. Further reading>>.

"Barden" - 980 - 990 AD

"Barden" was the ship of Earl Eirik of Norway and was is use around year 1000. It was large and had a high gunwhale. Its stem and stern was equipped with some kind of a rammer of made of iron. This ship was designed for attack at sea, as the rammer was used to cause damage to the hull of other ships. This ship was large, perhaps of the same size as "Ormen Skramme" and "Trana".
Snorre Sturlason about the ship: "Earl Eirik had a very large "barde" which he used in viking; it had "beard" at the top of both stems (fore and aft), and from this a thick ironplate as wide as the keel, reaching all the way down to the water." The english word "beard" is related to the norwegian word "barde", thus explaining the name of the ship.

"Visund" - ca 1020

"Visund" was the ship of king Olav Haraldson (St. Olav) of Norway. It was large, perhaps of the same size as "Ormen Lange". Its stem had a golden head of a horned vicent (european bison) instead of a dragons head, giving the ship its name "Visund". The ship is classified as a large "skeide" in the saga.

"Ormen" - 1060 AD

This ship was the ship of king Harald Sigurdsson Hårdråde of Norway (1015 - 1066). It was built in Nidaros (todays Trondheim) in Norway around 1060. The ship has the same name as the earlier "Ormen Lange", which was probably was the model for this ship. Snorre Sturlason tells about this ship in detail in his saga about Harald Hårdråde. It was a longship built as a "busseship", and of the same size as Ormen Lange. Elsewhere he also refers to the ship as a "drage" (serpent/dragon), thus beiing a longship. It had 35 "rooms" (sections) and was large according to this number. It was equipped with 35 pairs of oars. In the stem it had a golden dragon head and the stern was formed like hook, probably visualizing the tail of a dragon.

The sea launch of "Ormen" at the river Nidelv in Nidaros. Illustration by W. Wetlesen.

"Bøkesuden" - 1122 AD

The "Bøkesuden" was built in Nidaros in Norway by king Øystein Magnusson just before he died in 1123. The ship was of the same size as Ormen Lang, with a dragon head in the stern and a hook-like stern. Snorre Sturlason notes that the ship had a high gunwhale but rather low stem and stern. Perhaps an error in the design from the shipbuilders? The Bøkesuden was later used by king Inge Haraldsson Krokrygg and Erling Skakke.

"Reinen" - (The "Reindeer) 1130 AD

22 room (sections) large longship owned by king Sigurd Munn. This ship was known in the saga to have been faster than any other ship.

The ship of Earl Filippus - 1206 AD

This was a longship built in Tønsberg, Norway i 1206. It had very high gunwhale and 36 "rooms". This is even more than "Ormen Lange", suggesting a total length of perhaps 50 m. Its width is said to have been 25 "alen", equal to ca 15 m. It had two rows of oars with 48 oars in the upper row and 24 oars in the lower row. Each oar was operated by several men and was as long as 20 "alen". This gives a total number of 72 pairs of oars. With two men on each oar, it then had a crew of at least 144 oarsmen. With four men on each oar this doubles up to 288 men. Either way this ship was very large. It must have been very heavy with a rugged hull and probably with a jointed keel. It must also have been very expensive to keep in operation because of its large crew. Built in the 13th century, this ship was built after the viking age.

"Mariasuden"

36 room large. Mentioned in the saga in 1256. Built for king Håkon Håkonssen in Bergen.