It would be cool if they added some personalities to companions. For example, a character may be be extremely afraid of spiders, so if one attacks you, he/she might run away screaming. Or if you are approaching a large group of bandits, he/she might say "We are a bit outnumbered, I don't think it would be smart to attack them." Another example is being drastically outnumbered in a fight, and the companion saying "I'm out" and running away. However, I'm not saying all companions should be cowards, just the ones that are weak/don't like you that much. There could be giant Nords that aren't afraid of anything or people who really like you that may try to defend you to the death.
Also, I don't want them to be endlessly following behind you. If you stop near a cliff, they may walk away from you to peer off the cliff. Just little things like that that will make them feel more alive.