When the world was young the already ancient dragon, Zu, stole the Tablets of Law which regulated the order of the universe from the great god Enlil. The sun-god Ninurta was sent after - and killed - Zu and rescued the Tablets, thus preventing the universe from returning to the primordial chaos.

Tiamat and Apsu
From Babylonian mythology

The Babylonian creation epic, Enuma Elish, tells of how, in the beginning there was nothing save for two elements: Apsu - the male spirit of fresh water and the abyss, and Tiamat - the female spirit of salt water and chaos. Their children were the gods, but, becoming increasingly enraged by their offsprings' unruly ways, Apsu sought to destroy them. But the gods struck first and destroyed Apsu.

Tiamat lived on and plotted her revenge. She spawned eleven monsters to help her make war upon her children; the viper, the shark, the scorpion man, the storm demon, the great lion, the dragon, the mad dog and four nameless ones.
Marduk was the only god who fought Tiamat. There was an epic struggle but Marduk was finally able to shoot an arrow into her mouth which split her heart in two. He then divided her body into two parts - the sky and the land. Marduk cut the head off one of Tiamat's advisers and from the blood created humanity to serve as slaves to the gods.

Tiamat is portrayed in several different ways, but she was originally drawn as a four-legged creature with head and forequarters of a lion, a scaled body, feathery wings, an eagle's hind legs and a forked tongue. She also had a hide that was impervious to all weapons.

Azhi Dahaki
From Persian mythology.

Angra Mainyu, the Father of Lies, created Azhi Dahaki to rid the world of righteousness by extinguishing the light of a sacred flame known as The Divine Glory. When Atar, the god of fire, tried to save the flame, the dragon threatened to destroy the light of his fire forever, but Atar swore he would send his flames throughout the dragon's body. Azhi Dahaki drew back, but the divine hero Thraetaona bound and imprisoned the dragon on Mount Demavend near the Caspian Sea for the damage he had done to humankind on his evil quest.

It is believed that at the end of the world the dragon will be freed and, in his long repressed fury, will devour one third of all men and animals before the hero Keresaspa destroys him.

Azhi Dahaki appears as a fearsome three-headed dragon and his body is filled with spiders, lizards and snakes; if he were ever cut open then these venomous creatures would infect the world.

Illuyankas
From Turkish mythology

Illuyankas was a mighty dragon who was killed by the Hittite storm-god with the help of the goddess Inaras and her human lover Hupasiyas.

Yam-nahar
From Canaanite mythology

A seven headed sea dragon destroyed by the young god Baal.

Apophis (a.k.a Apep)
From Egyptian mythology

The spirit of darkness and death, Apophis was a huge sea-serpent that attempts to destroy the sun-god Atum-Ra during his voyage across the sky. He is attacked and slain by the children of Atum-Ra, or by Set - depending on what your source is.

Nidhogg (the 'Dread Biter') and Midgard's Worm.
From Norse mythology

At the 'still point of the turning world' there stands the ash tree Yggdrasil which supports the whole universe. There are three great roots of the tree, one of which reaches over Niflheim where Hel reigns as Queen of the Underworld. Beneath Niflheim the dragon Nidhogg gnaws at the root seeking to destroy the universe - which is why he's known as 'The Dread Biter'.

Midgard's Worm (a.k.a Jorungard's Worm) is a threat on a more earthly level. The Worm lies in the seas with its tail in its mouth, encircling the land, creating the oceans. Disaster would befall the world should the Worm's tail be removed from its mouth. Midgard's Worm meets its end at Ragnarok when it and Thor kill each other.

Fafnir
From Norse mythology

Fafnir was once a giant who killed his father in order to take the treasure he owned. To guard the ill-gained hoard he transformed into a dragon and carried it to a remote cave.

In another version of the legend - from the Volsung Saga which, incidentally, Wagner put to music as the Ring Cycle - Fafnir was transformed into a dragon after stealing the hoard of the dwarf Andvari which was cursed.

Either way, the dragon is eventually slain by Sigurd (called Siegfried in the German versions).

Ladon
From Greek mythology

Ladon was the guardian of the golden apples of the Hesperides and son of Mother Earth. He was slain by Heracles (Hercules):

"For 'twixt the sunlight and the shadow green
Shone out fair apples of red and gleaming gold.
Moreover round the tree, in many a fold,
Lay coiled a dragon, glittering little less
Than that which his eternal watchfulness
Was set to guard;"
-William Morrace, from 'The Life and Death of Jason'.

Quetzalcoatl
From Mexican mythology

Quetzalcoatl, the Lord of the Morning Star, was a benign serpent-like god worshiped by the Toltec Mexicans as the bringer of light to his people and fertility to the land. Sometimes he appeared arched across the sky, and other times he adopted human form - either a young man in a feathered cloak, or an old man with a broken walking stick and a white beard - and mingled amongst his subjects.

The Firedrake
From Norse mythology

This is the dragon that Beowulf fought his final battle with as the aging hero died of his wounds.