Jumping the flagpole in Super Mario Bros. is possible. This has been proven. Have you seen it on World 1-1, though? Well, thanks to this glitch, you will. [NSFW audio because this guy's nom de plume is 'Motherfucker Mike'] .
Mike says this video is 100 percent real and was done on a console, not on an emulator. The history of this urban myth says it was possible on world 1-1 but mythbusting attempts have only found it achievable on world 3-3, which has a high-reaching platform right before the jump, unlike 1-1's basic hill o'blocks.
I don't know if glitching the game counts as actually leaping it but, yes, there Mario goes, having slipped the surly bonds of 1-1, to put out his hand and touch the face of Miyamoto.
Jumping Over The Flagpole On Stage 1 in Super Mario Bros [Cinemassacre, thanks Manly McBeeferton]