If a Pokémon listens to its trainer, it is called an obedient Pokémon. But there are cases when a Pokémon doesn't listen to its trainer, this is called disobedience.
In the games[]
The Pokémon won't obey the trainer if the Pokémon is at a very high level and the trainer doesn't have enough badges to train it. This is done so that players won't transfer a high-leveled Pokémon from another game and beat the game. Having all eight badges makes all Pokémon obey a trainer. In the generation three games, Mew and Deoxys which were not met in a fateful encounter will always disobey the trainer, regardless of the number of badges they have.
In the anime[]
This is also carried into the anime as well. The main cause of Pokémon disobeying a Trainer is different for each, but it mostly stems from a Trainer being unable to control their Pokémon, most notably Ash's Charizard because it evolved at a rapid pace which would be hard for a new Trainer to control.
Pokémon which weren't or aren't obeying their trainers:
- Ash's Pikachu
- Ash's Charizard
- Ash's Primeape
- Ash's Snorlax (because it is mostly sleeping due to its nature)
- Misty's Psyduck (not purposefully)
- Misty's Gyarados
- Otoshi's Marowak
- Ash's Corphish
- Guy's Exploud
- May's Munchlax (not purposefully if its obsession with food)
- Dawn's Buizel (obeyed Ash)
- Ash's Infernape (Blaze activated)
- Dawn's Mamoswine
- Iris' Excadrill
- Iris' Emolga
- Luke's Zorua
- Bianca's Escavalier
- Iris' Dragonite
- Ash's Froakie (before joining Ash)
- Korrina's Lucario (in its Mega Evolution)
- Jessie's Mimikyu (unless if its fighting Ash's Pikachu)
- Ash's Lycanroc (before learning on how to control its rage)