Besides the gods, Greco-Roman mythology's most well-known figures are its heroes.
Heracles (or Hercules, depending on whether you prefer Greek or Latin) wasn't technically a god according to the Greeks. However, he was given divine honors in Rome, where he was worshipped as Hercules Invictus (Hercules the Invincible), god of heroes, sports, athletes, health, agriculture, fertility, trade, oracles and divine protector of mankind, at a men-only temple. Every day, a bull was sacrificed to him and the temple became an all-you-can-eat buffet - the entire bull had to be eaten within that day! No matter if or how Heracles was worshipped, his story remains the same.
Heracles, son of Zeus and his twin half-brother Iphicles, son of Amphitryon (a mortal), shared a mother, Alcmene, who was also mortal. Hera hated the fact that Zeus had cheated on her, so she sent two snakes to strangle little Heracles in his cradle. Alcmene and Hera were separately horrified to find him babbling happily with the two snakes dead in his hands!
Thanks to his demigod status, Heracles grew up to be strong enough that he killed his music teacher with a lyre when he got angry. He married a girl named Megara and had kids, but killed her and the children in a fit of madness induced by Hera (who evidently held grudges). After he returned to his senses, he put himself, at the order of the Oracle of Delphi - guided by Hera - into the service of King Eurystheus of Mycenae, his cousin.
Eurystheus assigned Heracles ten labors (but later increased the number to twelve after two labors were disqualified, because he was a jerk). These were as follows:
1. Kill the Nemean Lion and bring back its pelt. The lion's skin was impervious to weapons, so Heracles beat it with his club, then strangled it. The pelt later became Heracles' weapon-proof armor.
2. Kill the Lernian Hydra, a fearsome nine-headed serpent. Whenever one of its heads was cut off, two grew back. This labor was DQ'd because Heracles' nephew Iolaus helped him out by burning the Hydra's necks so the heads wouldn't grow back. Hera also sent a crab to pinch Heracles and distract him; Heracles simply crushed it. Hera put the crab in the sky as the constellation Cancer as recognition for its efforts.
3. Capture a horned doe sacred to Artemis with golden antlers and brass hooves. Heracles had to chase the doe for a year before he wounded and caught her!
4. Capture the Erymanthian boar, which was NOT your ordinary pig with tusks. On the way there, Heracles ran into some wine-starved centaurs while opening a cask at an inn; he had to fight them off but inadvertently killed a few. He gave both honorable funerary rights then set out to capture the boar, which he soon did.
5. Clean the stables of King Augeas, which hadn't been cleaned for thirty years. Heracles diverted two nearby streams to them and cleaned them in one day. This labor was disqualified because Heracles asked for payment.
6. Chase away the Stymphalian Birds, who had feathers as sharp as arrows. He was quite puzzled as to how to complete the task, when suddenly he saw Athena in front of him. She gave him a pair of bronze clappers made by Hephaestus, and he scared the birds away with these.
7. Capture the Cretan Bull. Minos, the slightly messed-up king of Crete, had promised to sacrifice this magnificent bull - which emerged from the waves - to Poseidon but killed an inferior bull instead. As a result, the first bull went mad and started wrecking the island. (Minos later became known for housing the Minotaur, the result of another cheating sacrifice to Poseidon.) Heracles captured and tamed the bull, but Eurystheus released it, upon which the poor animal went crazy again. It was dispatched years later by Theseus.
8. Capture the man-eating mares of Diomedes, a son of Ares. Heracles first captured Diomedes and gave him to his own mares, so the mares became suddenly tame. Diomedes' people attacked Heracles, but the latter's friend Abderus won a battle with them using the mares. However, the mares then killed Abderus. Heracles brought the horses to Eurystheus, who let them loose on Mount Olympus. The mares were later eaten themselves. (The irony.)
In between his eighth and ninth labors, Heracles joined the Argonauts with his friend Hylas. However, Hylas was drowned by water nymphs at Chios and Heracles was left behind looking for his friend. As he trekked back to Greece, he performed his ninth labor.
9. Steal the girdle (really, a belt) of Hippolyta, queen of the Amazons. Heracles wooed Hippolyta into giving him the girdle, but Hera spread a rumor among the Amazons that Heracles was out to kill their queen. A battle ensued, which Heracles won. He was able to leave with the girdle after killing Hippolyta and fighting off some other Amazons.
10. Capture the red oxen of Geryon, a three-bodied, three-headed, and twelve-limbed giant. The oxen were guarded by another giant named Eurytion and a two-headed dog named Orthrus. On the way to complete this labor, Heracles erected the pillars named after him on each side of what is now the Strait of Gibraltar. As soon as Heracles arrived, he was attacked by Eurytion and Orthrus, but Heracles killed both. He rounded up the herd, but before he left he fought and killed Geryon. Heracles and the oxen swam to Mycenae, where Eurystheus sacrificed the oxen to Hera. Then he imposed two more labors on Heracles because he refused to count the second and fifth for reasons described above.
11. Retrieve the golden apples of the Hesperides, daughters of Night. These apples, which conferred immortality for a period of time, were guarded by a dragon called Ladon. Heracles didn't know where the garden where the apples grew was, so he had to go through a lot before he could finally get there. During his wanderings, he freed Prometheus (the Titan who brought humans fire). Once at the garden, he acted on Prometheus's grateful advice and had Atlas, another Titan who held up the world nearby, put the dragon to sleep and get the apples for him while Heracles held up the world. When Atlas came with the apples, he said he didn't want the world back after tasting freedom. Heracles replied that he needed to get a pad for his head, and so was able to escape. Back in Mycenae, Eurystheus gave Heracles the apples, which wound up on Athena's altar and then back in the garden.
12. Capture Cerberus, the three-headed dog who guarded the underworld. After becoming initiated in Demeter's Eleusinian Mysteries, Heracles headed for the nearest opening to the Underworld. With Hermes by his side, he headed in and subsequently started freeing tormented souls like Ascalaphus, the gardener who had revealed that Persephone had eaten pomegranate seeds in Hades, and Theseus (alive but chained to a bench after trying to abduct Persephone). Heracles then headed to Hades' dark palace and shot the god of the underworld in the shoulder with a dart, then asked to borrow Cerberus. The god replied yes, on condition that the dog was not harmed. Heracles took Cerberus to King Eurystheus, who was so horrified at the sight of the dog that he had Cerberus returned to Hades! With this Heracles' first period of servitude ended.
Years later, living with his second wife Iole, princess of Oechalia, Heracles went crazy again (thanks, Hera) and killed his brother-in-law Iphitus during an attempt to thwart the thief Autolycus. Heracles became the slave of Omphale, queen of Lydia (modern-day Turkey) for three years, at the advice of the oracle of Delphi - this time without Hera. He helped her get rid of bandits and even participated in the Calydonian Boar Hunt, and when she figured out his identity she released him from slavery and made him more of a husband that a slave. Sometimes they traded places for fun (which actually sounds hilarious)! Once the remainder of his three years in Lydia were up, he headed home and married Deianira, princess of Aetolia. Shortly after their marriage, Heracles left Calydon for Trachinia with his wife and son because he'd accidentally killed a young servant at a banquet. On his way, they came to a river at which a centaur was the ferryman. Heracles forded the river with his son, but the centaur had to carry Deianira across - and then tried to abduct her because she was so pretty. Heracles shot the centaur, called Nessus, with a poisoned arrow. The dying, vengeful centaur told Deianira to take the blood spilling from his body and use it as a love charm if Heracles ever wanted another woman. Soon enough, he did, and Deianira smeared the blood on him. However, the blood was poison, and it burned away Heracles' skin. Deianira realized what she'd done and killed herself. Soon afterward, Heracles died. Nobody but his friend Philoctetes had the courage to light his funeral pyre. All of a sudden, there was a flash of lightning, and Heracles was carried up to Olympus. Although not officially a god (yet), he was given Hebe, goddess of youth, for a divine wife. She was his half-sister, but that didn't seem to bother anyone!
Perseus's grandfather, Acrisius, heard from an oracle that his grandson would kill him. Naturally, he pulled a Mother Gothel and imprisoned his only child, his daughter Danae, in a tower. Zeus visited her concealed in a drop of golden rain, and they "did it" and had a baby - Perseus. Nine months later, Acrisius found out what had happened, so to prevent his own premature death, he put Danae and Perseus in a chest and set it afloat. They landed on the island of Seriphus, ruled by the evil King Polydectes, and were taken in by a fisherman named Dictys.
20 years later, Polydectes tried to get rid of Perseus, so he could have Danae all to himself. He sent him to fetch the head of Medusa, whose gaze turned people to stone. The gods were on Perseus's side - Athena gave him a mirrored shield, Hermes gave him winged sandals, and Hades gave him a cap of invisibility and a bag that could hold anything. Perseus used the sandals to fly to Medusa's cave, and the shield to avoid looking at Medusa herself, just to look at her reflection to check her position. (She was asleep.) Perseus put on his cap so the other two Gorgons wouldn't see him, cut off Medusa's head, put it in the bag, and used his sandals to fly off. On the way back, he rescued a princess of Ethiopia named Andromeda. The princess's mother, Cassiopeia, had boasted Andromeda was more beautiful than the sea nymphs, and an angry Poseidon had sent a sea monster named Cetus to eat Andromeda. Perseus turned Cetus to stone with Medusa's head, and asked for Andromeda's hand in marriage in return for saving her. Her parents said yes, so the couple married. At the party, Andromeda's former fiance and his buddies showed up and demanded Andromeda. Perseus told her and everyone besides the fiance and his group to close their eyes, and in seconds, the party-crashers became a circle of stone.
A few days later, King Polydectes was summoned to the throne room and was shocked to see Perseus standing there with Andromeda. Perseus told Andromeda to close her eyes and pulled out Medusa's head. Polydectes and his cronies were turned to stone. Perseus, Andromeda, Dictys the fisherman, and Danae then ruled Seriphus. Medusa's head, by the way, didn't stay with the new royal family; Athena put it in her shield for safekeeping.
The prophecy of Acrisius eventually came true... 20 years later, and without either party knowing it. Perseus entered a discus contest in Larissa, and Acrisius, on the run from his now-famous grandson, attended the match. Perseus's discus blew off course and hit Acrisius, who then died of a heart attack.