Pokemon with high affection due to Pokemon Amie (3 hearts or higher) shake. They also "wait for your directions" rather than just saying for you to choose a move. AND FINALLY, they can sometimes (my Pikachu has done it twice so far) endure hits, leaving them with 1 HP left when it would KO Pokemon with lower affection. A heart comes up from their in battle sprite and I believe it says something like "name endured the hit to show your name its tough side!"
Hope this helped :)