Dark Void:
Dark Void puts the foe to sleep. In a Double Battle, Dark Void will hit both foes with an accuracy of 80% for each Pokémon.
Now that is devastating. Putting both foes to sleep in one turn with 80% accuracy is totally OP, and Smeargle can almost always get one off with a Focus Sash.
Sky Drop:
Due to this glitch, the move Sky Drop was banned in Wi-Fi Random Matches starting November 10, 2010.
This glitch can only occur in Double and Triple Battles. It is activated when Gravity is used while two Pokémon are in the semi-invulnerable state after Sky Drop is used. Gravity will bring the user of Sky Drop down, while the target will be stuck in the semi-invulnerable state, unable to move until it is knocked out.
Basically cripples a Pokemon for the whole game if you can pull it off.
Chatter:
The reason Chatter was banned is because you can record your voice saying inappropriate things. It still doesn't make any sense why Chatot was banned though...