In the biography of Dumbledore (by Rita Skeeter) it is said that Dumbledore finally decided to confront his one time friend Gellert Grindelwald, who at the time was powerful and was in possession of the Elder Wand.
After Dumbledore defeated him in their famous duel, Dumbledore claimed his wand, the mythical Elder Wand and stopped using his old wand.
So what did he do with his old wand?