There is also the tale of Hercules, the demi-god, son of Zeus and Alcmene, a mortal woman. Zeus came to her, disguised as her husband, Amphitryon, and had sex with her, impregnating her with Hercules.
The story goes that Hera loathed Hercules (as she hated most of the women Zeus slept with and their children -- and Zeus's affairs always produced offspring). One day, after he'd grown up, Hera put him into a sort of crazy rage trance and he killed his wife, Megara, and their sons. He came to just after the killings, and found their bodies and himself covered in their blood. Theseus actually took him in because he felt that Hercules should not be held responsible for the murders because he wasn't aware of what he was doing. However, the oracle at Delphi said that Hercules needed to be purified, and she sent him to his cousin, the King of Mycenae, Eurystheus. Encouraged by Hera, Eurystheus gave Hercules many tasks called the "Labors of Hercules." Each one was believed to be impossible, and so Hera was clearly hoping that Hercules would die in the attempt to complete them.
First, he kills the lion of Nemea, who could not be wounded by weapons, so Hercules choked him. Second, he killed the Hydra, a monster with nine heads. Each time he struck one of its heads off, two grew in its place. So Hercules cauterized the stump after he struck off the head, and this prevented regrowth. Third, he brought back Artemis's sacred golden-horned stag, but he had to capture it alive. This took a year of hunting. Fourth, he captured a great boar, driving it into the snow and trapping it. Fifth, he cleaned the Augean stables in a day by diverting the course of two rivers so that they would flow through the stables and carry away the refuse. Sixth, he drove away the Stymphalian birds, with a little help from Athena. Seventh, he stole a beautiful bull given to Minos by Poseidon. Eighth, he drove away the man-eating mares of King Diomedes. Ninth, he brought back the girdle of Hippolyta, Amazon Queen. Hera made this one tough by making the Amazons believe that Hercules was actually going to steal their queen. Tenth, he brought back the cattle belonging to Geryon, a three-bodied monster. Eleventh, he brought back the Golden Apples of the Hesperides. To do this, he had to trick Atlas. Lastly, he had to go to the underworld and bring back Cerberus, the three-headed dog that guards the gates.
Hercules isn't known for his intelligence, but he is credited as being the "greatest hero in Greece" (except for in Athens, because Theseus is preferred there) due to his physical strength, bravery, and passionate nature.
You could also check out the story of Odysseus, the hero on whom The Odyssey is based, as well as Jason and the Argonauts who sailed the Argo on the Quest for the Golden Fleece. What ties these heroes altogether, with the exception of Theseus, is their bravery (even bravado) and their brawn; Theseus is best known for his intelligence and diplomacy. They all complete physically, and mentally, demanding tasks and are believed to have made Greece a safer place for all.