Ludovic "Ludo" Bagman is a fictional character who appears in Harry Potter and the Goblet of Fire.
He is the head of the Department of Magical Games and Sports in the Ministry of Magic, and formerly was a highly succesful Beater, making him a minor celebrity. Ludo appears to be a jovial if absent-minded man, with perhaps a hint of too many Bludgers to the head. He was accused of being a Death Eater about 13 years before Goblet of Fire, having unknowingly (and unwittingly) given information to a real one, but was subsequently acquitted.
Bagman loved betting, which got him in financial trouble so severe that he paid some of his creditors (such as Fred and George Weasley) with disappearing Leprechaun Gold after a round of gambling on the Quidditch World Cup. After the World Cup, the goblins—his worst and most enthusiastic creditors—took all the gold he had and it still didn't cover all his debts. His behaviour towards those demanding their money worsened as the situation did, which may indicate that his good-natured demeanor is a façade, or that he doesn't respond well to pressure.
To make it up, he made a bet on the Triwizard Tournament (of which he was one of judges). He bet the goblins that Harry Potter would win. He tried to help Harry over the course of the Tournament and gave him a perfect score in the First Task even though he got hurt. Harry did touch the Goblet, but Bagman didn't win the bet: the goblins argued that Harry had tied with Cedric Diggory. Bagman presumably doesn't now have so much as two Galleons.
As with many J. K. Rowling characters, Bagman's name gives clues to his nature. Ludo in Latin means "I play games", and a bagman is one who engages in extortion or racketeering.
