The legend of Medea killing her and Jason's sons is probably one of the most famous acts of filicide in Greek mythology. Pretty much as soon as you say Medea's name, people go, "Oh, that woman who killed her kids?" Though Medea might be one of the most famous murderous mothers of mythology, she's definitely not the only one. Another big example would be Agave, who, driven insane by Dionysus, was said to have ripped the head off of her son, King Pentheus. Of course, Agave doesn't have as bad a reputation as Medea, probably because her son was all grown up, and, more importantly, because she was supposedly possessed by a god
There's also a long list of Greek mythological mothers who tried to kill newborn babies by "exposing" them, which means leaving them in the wilderness to fend for themselves. Jocasta, the mother of Oedipus, signed off on having his ankles pinned together and left on a mountain to die. There's also Heracles's mother, Alcmene, who abandoned him in a field for fear of the wrath of Hera. In both these cases, however, the ladies failed to kill the children, and their little boys eventually came back to them. In Alcmene's case this ended up being a good thing, while in Jocasta's case it was a bad bad bad thing... did we mention in was bad?
The women are definitely not the only ones in Greek mythology who killed their children. The men did took part in their fair share of filicides as well. There was Agamemnon who sacrificed his daughter, Iphigenia. This in turn caused his wife, Clytemnestra, to kill him, and his son, Orestes, to kill Clytemnestra. So, that's a filicide to mariticide to matricide situation. (Dude.) Probably, the most famous child killer was the great hero Heracles, who was driven insane by Hera, causing him to slaughter his little ones.
In Other Cultures...
Of course, the Greeks weren't the only ones with myths of filicide. One example is happens in the Celtic legend of the hero Cuchulain, who is said to have accidentally killed his son, Connla, not knowing who he was. There's also the Biblical story of Abraham and Isaac, in which God asks Abraham to sacrifice his son Isaac in order to test Abraham's faith. At the last minute, however, God tells Abraham not to go through with it. Also in the Bible, there's the story of Absalom, who rebels against his father, King David, and is killed by David's men in battle.
Latin American folklore has a story that's actually really similar to the myth of Medea. In this story there is a fabulously beautiful and incredibly vain woman named Maria (rhymes with Medea), who marries a handsome ranchero. For a while, the two are happy, and they have two kids (like Jason and Medea). Eventually, though, the ranchero gets tired of Maria. He only pays attention to the children and starts making plans to marry another woman (sound familiar?). Crazy with jealousy, Maria throws her children in a river, and they drown. Afterwards Maria feels so bad that she kills herself as well. Now, it's said that a woman in white, whom people call "La Llorna," walks up and down the river crying for her children. Mothers tell their children not to go out at night, or else La Llorna might snatch them.