I know that you can use all HMs out of battle, but there are some like dig and headbut that you can use out of battle. Does anyone know what all of these moves are and in what games they can be used out of battle?
Great question! Here are the ones I can think of, there may be more:
Dive (HM in Ruby/Sapphire, to allow you to go underwater)
Dig (escape from caves)