Jörmungandr and Nidhoggr

[Dragons in mythology]
Two major Norse dragons: (viking dragons)
Jörmungandr:
Also spelt: Jormungand, Jormungander, Jormungond etc, and also known as The Midgard Serpent, or Midguard Serpent. (sometimes Midgard Wyrm).
He is a mighty dragon that encircles the world, stopping the sea from falling over the edge. Like most giant world-hugging snake-dragons he holds his tongue in his mouth as a symbol of eternity. 
He is the son of the Trickster God, Loki, and a giantess, Angroboda, and is the middle child of his strange family. His older brother is the daemon wolf, Fenrir (Fenris) and his younger sister is Hel, who is half a beautiful woman and half a corpse (sometimes the split is down the middle, sometimes at the waist.)
Once upon a time Jormungand would live in Angraboda's house, but that was before the Gods found out about Loki's affair (he was married to Sigyn, not Agraboda). When they heard about the three monstrous children they charged into Jutunheim and broke into Angraboda's house. They knew the children would be too evil to be running around, so they dealt with each one in a different way. The dragon-snake was grabbed by Odin and thrown into the sea.
It was there that Jormungand grew into a huge size, and he had to coil around Midgard (the 'Middle Earth', below Asgard, above Hel, between Niflheim and Muspell) to avoid falling off into space. When he was large enough he began to eat his own tail.
Jormungand, as a giant snake at the edge of the world, doesn't get involved in a lot of myths. But he does get a bit of excitement now and again.
For instance, there was a time when Thor wanted to go to a city in Jutungheim called Utgard. He and his friends (Loki, Thialfi, and Roskva) had a long journey and arrived. Within the halls of Utgard the king, Utgard-Loki, gave them many challenges. Thor got the most: he had to prove his drinking skills, lift a cat off the floor and fight an old woman. The small drinking horn somehow contained too much liquid for Thor to get 'down in one', the cat proved to be impossibly heavy (too much Wiskas?) and the old lady effortlessly beat him black and blue. At the end of the story it is revealed that the contest was rigged to be impossible; the man who won Loki's eating competition was Fire, the man who outran Thialfi was Thought, and drink in Thor's horn was the Sea, the old lady was Old Age, and the cat was Jormungand.
Another story about the World Serpent was that of a doomed fishing trip. The Gods had run out of mead, and could not make more without a cauldron. Tyr (warrior god) had some relatives who were giants, and therefore had a cauldron big enough to make enough mead, so he and Thor went off to steal it. During the trip they get distracted, and Thor is invited by Hymir (owner of the huge cauldron) to go on a fishing trip. He helps himself to bait from Hymir's livestock, taking the head of a prize bull. While the giant catches a few whales, Thor manages to fetch Jormungand from the deeps, but the serpent gets away (in some versions Hymir cuts the line out of fear).
Jormungand also features in Ragnorok, the end of the world. He will rise out of the water and head to a place called Vigrid alongside his brother, Fenrir. Jormungand will be killed by Thor, but his venom will kill Thor a few minutes afterwards.

Nidhogg:
Many ways to spell his name: he is a giant wyrm that eats corpses. 
He eats the roots of Yggdrasil for eternity, wearing away the roots of the universe.
Not much else to say about him really, as he does not feature in any myths.