While Alexander the Great, that real, Hellenistic conqueror, with a flowing leonine mane and youthful beauty, appealed to ambitious men like Julius Caesar, some of the Roman emperors tried to associate themselves with one specific Greek legendary hero -- Hercules, whom, incidentally, Alexander emulated.
As is shown in this picture of Commodus dressing up as Hercules, the signature piece of apparel for the hero was the lionskin, especially the head that partially covered the hero's own. The hero might have been known for his prowess with the poison-tipped arrows he bequeathed to Philoctetes, but he is usually shown with another weapon, a club, as you'll also see in the Commodus picture. When Diocletian was creating the rule by four known as the tetrarchy, he styled himself Jovius, for Jupiter, and gave the name of one of his most important sons, in the form Herculius to his second in command, Maximian.
There are enough stories and variations on the theme to last a researcher a lifetime, so I frequently update my pages on him. The basic page is now quite long. You can see it here: Who Is Hercules?.
I think, however, most people who come to this site want information on the stories about him, rather than his identity and birth. They want to know all about his superhuman adventures, and in particular, the 12 Labors, that should have been only 10. Do you know why there were more than 10?
For my page with pictures and descriptions of each of the labors, I located a couple of better illustrations than the ones I had originally used and updated the corresponding descriptions. See: Illustrated Labors of Hercules.
I said Hercules was important and of general interest, so here are some previous myth Mondays featuring Hercules: