The man with the most unfortunate name in the Wizarding World is also the Minister of Magic—you know, like the Prime Minister, but for wizards. He doesn't have a lot to do in Goblet of Fire, but he shows up at big events like the Quidditch World Cup and the Triwizard Tournament.
He's responsible for the decision to keep the Triwizard Tournament going, even after Barty Crouch Senior ends up dead in the woods. He and Dumbledore get into a heated debate over it:
DUMBLEDORE: A man has died here, Fudge. And he won't be the last. You must take action.
FUDGE: I will not. In times like these, the wizard world looks to its leaders for strength, Dumbledore!
DUMBLEDORE: Then for once show them some!
FUDGE: The Triwizard Tournament will not be canceled. l will not be seen as a coward!
DUMBLEDORE: A true leader does what is right, no matter what others think.
FUDGE: What did you say? What did you say to me?
Of course, when the tournament results in Cedric's death and Voldemort's return, Dumbledore is proven right…and we'll have to wait until the next film to see whether Fudge acknowledges that fact. (We aren't holding our breath.)