kinda a repost :/
By the time you get Dragon Claw, you've really only got to get through the Pokemon League. Dragon Claw is pretty solid on Charizard because it's super effective against Lance's Dragonair and Dragonite, and it's decent neutral coverage against pretty much everything else. There's no reason not to put it on Charizard -- it's an effective use of a TM due to Charizard's Special Attack and ability to deal with most of Lance's team.