while I couldn't say what game had the worst story I can say it completely depends on whether its what game has the worst story that actually cares about story (final fantasy games, most RPGS), or what game has the worst story that is meant to drive the game along (Halo, Borderlands most shooters) or what game has no story and just doesn't care (Pac-man, Tetris, most old school games)
I'm going to go ahead and say Mario because it felt like it was meant to be in the last section but for some reason it's treated as though it belongs in the first ><
Also the reason you don't see what kind of game has the worst story, worst game play, worst graphics etc. etc. is because there are allot of games who just don't care about those kinds of things. Pretty much the same reason we have a world record book for who is the best at some things but not a book for who is the worst.
P.S. those who say the final fantasy games had bad stories, try actually paying attention they kind of require that... Actually Final fantasy XII and XIII where a bit TO hard to understand so I agree with you there.