There are many monsters in Greek mythology. I will tell you about the ones I know and a little info about them.
Gorgons:The most well known is Medusa.
Furies:The three sisters made from Uranus's blood to torment Cronos.Alecto, Tisiphone, and Megaera.
The Graeae: Three sisters who have one tooth and eye between them.
Sirens: Giant bird looking women who use their sweet voices to lure people to their island. When they do the eat them.
Harpys: Know as the women death birds who snatch food and even people
Minotaur: Part man, part bull who dwelt in the middle of the labyrinth, he was eventually killed by Theseus
Chimera: The offspring of Typhon and Echidna, lion fronted, snake behind, and goat in the middle
Cerberus: Is the giant three- headed dog that guards the underworld.
Sphinx:A half woman, half lion creature that asks anyone she captures riddles, and if they can't answer, she eats them.
Cyclopes: have one eye, look like humans, and are master smiths (they made Zeus' famous thunderbolt)
Centaur: Half horse, half human
Hydra: Many headed creature. when you cut off one head 2 new heads appear, one of the twelve labors of Heracles
Orthrus: The twin of Cerberus, except it has two heads not three
Nemean Lion: Vicious monster with fur like steel. First of Heracles's 12 labors
Scylla and Charybdis: Guardian of the Sea of Monsters
Boar of Calydon: It was created to ravage the land of Calydon because its king failed to honor the Olympian Artemis which caused the Carydon hunt in which the boar was killed.
Stymphalian Birds: Metallic birds that Heracles had to defeat for one of his labors.
Hundred Handed Ones:Relatives of the Cyclopes, but huge and have a hundred hands.
Some of these monsters are good some are bad and a few are more like guardians.