Cubone has appeared briefly on several occassions; mostly in New Beginnings. It's very scared and dislikes battling, often sticking by Hayley rather than with other Pokémon.
Cubone, like most of its species, is a very lonely Pokémon who rarely interacts with others. Despite this, it's shown that it's genuinely happy not socializing with others. It spends a lot of its time with Hayley, often out of sight.
Thanks to the skull of his dead mother he wears, he is able to communicate with the dead, although usually he gets distracted by trying to speak to his mother.