Atlas

Atlas fought for the Titans in the war against the Olympians, and in some accounts led them. When it was lost, Zeus gave him a sentence rather than a prison: he was made to stand at the western edge of the world and hold the sky up, keeping it separate from the earth forever.

The common image is wrong in a specific way. Atlas does not carry a globe of the earth; he carries the heavens. The confusion comes from Renaissance map books that printed a picture of him on the title page, which is also why a book of maps is now called an atlas.

He gets two visitors. Heracles, needing the golden apples of the Hesperides, offers to take the sky for a moment if Atlas will fetch them, since the apples grew in his daughters' garden. Atlas agrees, comes back with the fruit, and announces he will deliver them himself and leave Heracles holding it. Heracles agrees pleasantly and asks him to take it back just long enough to pad his shoulders — and then picks up the apples and walks away.

Perseus fared worse in Ovid's telling: refused hospitality, he showed Atlas the head of Medusa and turned him into the mountain range that still carries his name.

His name probably means 'the one who endures', and endurance rather than strength is the point of him. Nothing in the myths suggests Atlas could put the sky down if he tried harder; the sentence is designed so that effort is irrelevant. That is the difference between his punishment and Sisyphus's — Sisyphus gets to fail repeatedly, while Atlas is not permitted even that.