Within one of the houses in Fuchsia City, you will find a man that will be willing to remove any attack that a Pokemon of yours known. He can remove moves learned by leveling up and from TMs, as well as from HMs that cannot be removed any other way. This character is key as you will not be able to transfer any Pokemon that knows an HM Move to Pokemon Diamond, Pokemon Pearl, Pokemon Platinum, Pokemon HeartGold or Pokemon SoulSilver.