This is not a super-fun group, that's for sure. When the Oracle of Delphi said that little baby Oedipus would grow up to kill his father and sleep with his mother, his parents did what any sensible parents would do. They pinned his ankles together and ordered a slave to abandon him on a mountain.
This Prince of Troy is most famous for sparking the Trojan War when he took off with Helen of Troy even though she was married to a big, burly Spartan named Menelaus. Just like with Oedipus, Paris was abandoned on a mountain because of a prophecy. Before he was born, his mother, Hecuba, had a dream that she gave birth to a flame that destroyed all of Troy. A seer told her that this dream meant that Paris would be the cause of Troy's downfall. So it was off to the mountainside for little baby Paris. Paris was saved by a friendly she-bear who didn't mind suckling humans, and (like Oedipus) he was eventually rescued from the wilderness by a shepherd.
One of the toughest ladies in Greek mythology, Atalanta was abandoned by her father King Iasus because he wanted a son. Just like Oedipus and Paris, she was left on a mountain to die. Also like Paris, she survived because she was suckled by a she-bear. (Man, there were a lot of overly friendly she-bears back then.) Eventually, Atalanta was taken in by some hunters, and she became one of the best huntresses to ever string a bow.
This hero of heroes is the son of Zeus and the beautiful mortal woman, Alcmene. His mom was more than a little freaked out when he was born because Zeus's wife, Hera, was pretty famous for being the jealous type. Hera had already tried to kill Alcmene and Heracles by interfering with Heracles' birth. Fearing further nastiness from Hera, Alcmene abandoned Heracles in a field. (What? No mountain?) Luckily for Heracles, Athena came along and saved him by tricking Hera into breastfeeding him and eventually dropping him back off with his mom.