Heroes
The ancient Greek definition of a hero does not match the Judeo-Christian definition of a hero. Generally, in the Western world, heroes should be brave yet humble, inspiring yet self-effacing. Suggest to an ancient Greek hero that perhaps he shouldn't boast so much, or that he should be a bit more altruistic, he would have laughed in your face--or ripped it off, depending on his mood.
In fact, the heroic culture to which figures like Herakles, Achilles, and Odysseus belonged encouraged such wholesome activities as looting, rape, and boasting. In the absence of permanent armies and coinage, raiding and pillaging was the equivalent of the defense budget for the Mycenaean world. The king had to lead his fighting aristocracy against some neighboring kingdom or tribe every once in a while to let them blow off steam and reap some material reward, or he would very quickly find himself a king without followers, a kingdom, and a pulse. As for boasting, in an age before Facebook and CNN, heroes had to see to their own PR, and hope that some prestigious bard would pick up the story and spin it into Late Bronze Age ratings gold.
It's worth keeping in mind that most of the Greek heroes, if they were alive and committing atrocities working today, would most likely find themselves on Death Row or in a maximum security State Penitentiary.