Playing Against Type: Often cast as tough cunning heroes (and later wise mentors), Connery goes in the opposite direction with Indiana Jones and the Last Crusade where he plays a bumbling, tweedy, mildly absent minded professor not prepared for his son's more adventurous escapades. And he is absolutely HILARIOUS in the film.
He also turned down the role of the Architect in The Matrix Reloaded and Revolutions. He said that both the Matrix and Lord of the Rings scripts made absolutely no sense to him when he read them.
Ian Fleming, the creator of the James Bond character which made Connery famous, reportedly disliked Connery being chosen for the role at first because he happened to be a big, stocky Scottish guy with a rough and rugged face as opposed to the more refined look Fleming imagined for the character. Fleming later changed his mind after actually seeing Connery in action and, before he died, he even retconned Bond's origin to give him Scottish heritage (possibly just to make sure the cinematic and literary incarnations would match since he undoubtedly realized that the films would reach more people than the books).
During the filming of Zardoz Connery found out that John Boorman paid a guy 5000 bucks to be his chauffeur. Seeing as how it was a relatively low budget film he then proposed that he drive(s) the car himself, the chauffeur is fired and Connery and Boorman split the 5000 between them. That's just how cool Sean Connery is.
Also around the time he was working on the film he and Boorman were mobbed while attending a rugby game, which frightened Boorman, but Connery raised his hand to the mob of fans and shouted STAND BACK! and, according to Boorman, the crowd parted like the Red Sea before Moses, and they were allowed to pass.
During the filming of Another Time, Another Place (1958) gangster Johnny Stompanato stormed the set and threatened Connery with a gun, believing him to be having an affair with costar Lana Turner, Stompanato's girlfriend. Sean Connery took his gun from him and beat him up. That's how cool Sean Connery is.
He was named People Magazine's Sexiest Man Alive at the age of 58, a record that has yet to be topped.