The dragons of Greek mythology were different than in common mythology. They were serpentine monsters and most of them weren't accounted to be flying around like dragons in other mythologies. The Greeks separated dragons into three family groups which included the serpent-like Dracones, the marine-dwelling Cetea and the she-monster-like creatures Dracaena.
Dracones were giant serpents, usually possessing deadly venom or multiple heads.
Colchian Dragon - never-sleeping dragon which guarded the Golden Fleece in Colchis. It is said that the dragon never lowered its vigilance. During the retrieving of golden fleece, it was put to sleep by Orpheus' soft tunes and Medea's magical potion.
Cychreides - a dragon which terrorised Salamis before being slain by Cychreus whom the dragon got its name after. There is another version of story which tells us that the dragon was captured by Eurylochus who gifted it to Demeter.
Ismenian Dragon - a dragon which guarded the sacred spring of Ares near Thebes. It was slain by Cadmus in his quest of founding Thebes when he went after his men who did not return, after sending them for water.
Ladon - a serpent-like dragon with hundred heads which guarded the apples of Hesperides. It is said that the serpent did not need to sleep entirely. While sleeping, at least couple of heads were always awake and focused.
Lernaean Hydra - a nine-headed dragon with deadly venom which guarded the springs of Lerna. It was slain by Heracles in the second of his twelve labours. However, he was having help from Lolaus and therefore this labour didn't count.
Cetea were sea monsters. They usually featured in myths of a hero rescuing a sacrificial princess.
Ethiopian Cetus - a sea monster sent by Poseidon to ravage Ethiopia, after Cassiopeia bragged that her daughter Andromeda was more beautiful than the Nereids, relatives of Poseidon. The monster was later slain by Perseus who came to rescue Andromeda.
Trojan Cetus - a fearsome sea monster sent by Poseidon, after the king of Troy refused to pay him for the walls which the god had helped to build there. The monster was slain by Heracles who, like Perseus, came to rescue Hesione from being sacrificed.
Dracanea were creatures displaying characteristics of a woman and a serpent.
Echidna - a half maiden and a half serpent who was nothing like men nor undying gods but still immortal and never aged. It is said that she was a consort of Typhoeus or Typhon and bore him Orthus, the two-headed dog.
Campe - a she-dragon with a beautiful face and upper body but had a monstrous viperish tail. She was tasked by Cronus to guard the gates of Tartarus where he imprisoned the Cyclopes and Hekatoncheries. It is said that she was killed by Zeus who came to rescue the prisoners and make them his allies.
Scythian Dracaena - a she-dragon that ruled the lands of Scythia. It is said that she mated with Heracles who agreed to a compensation of giving him back a couple of mares from Geryon's flock that she captured. After, she gave birth to three sons, Agathyrsos, Gelonos, Skythes.