Animals might not be able to speak, but they do communicate and form bonds. I think it would make sense if, while working on improving the communication system for sapients, some of the same behaviors could be applied to non-sapient creatures as well, even those that spawn in the wild.
Animals in DF already are generated with diverse personalities based on the same values as sapients, and the average values of a given species can be adjusted in the raws. They can also become stressed and go insane, but only a handful of things (such as being held in a cage) seem to bother them, and their irritation at being kept in crowded pastures still runs off of an old, simplistic system. But it would make sense to apply some of the same thoughts to animals that sapients feel, and adjust them by the same personality tokens. GREGARIOUSNESS could affect how quickly animals become upset about being around others - or could even make them prefer company, just like sapients with high levels of this trait prefer crowded tables, so flocking animals like sheep would have high levels of this trait. Animals could become distressed seeing members of their own species die, perhaps adjusted by the EMPATHY token. EMOTIONALLY_OBSESSIVE animals could form personal ties with members of their own (or other) species, become distressed when separated from them, and would be much easier to train due to forming bonds with their trainer. DUTIFULNESS could also affect training behaviors, making animals less likely to forget their training and go wild. Animals with high ANGER_PROPENSITY would be prone to lashing out when overstressed, which would work pretty much exactly the same way as tantrums. VENGEFUL animals would be prone to remembering grudges and attacking those who harmed them in the past, like elephants are famous for.
Instead of having fixed TRAINABLE_HUNTING and TRAINABLE_WAR tags, the trainability of any given animal would be flexible, and based on their personalities (and the skill of the trainer). Dogs, for instance, could have high EMOTIONALLY_OBSESSIVE and DUTIFULNESS levels, making them easy for a trainer to bond with and therefore easy to train for any purpose. BRAVERY or VIOLENT would be important for war training, while high SINGLEMINDEDNESS could make better trained hunters. There could also be more interesting traits, such as PRIDE or ENVY_PROPENSITY, that might have an effect on training as well, particularly for fantastic creatures such as dragons.
If personalities are transmitted genetically, this would also allow selective breeding to make formerly untrainable animals trainable over multiple generations, or to selectively breed them for particular behaviors and traits.
Also, for adventure mode in particular, it would be nice to see more use of the 'sound' system. Perhaps animals could 'talk' to each other just like sapients - not spreading rumors or anything like that, but enough to convey simple messages - with specific tags describing the sounds made to convey each 'message'. So we could have things like INTIMIDATE (like 'barking' in place of 'I've killed so-and-so', when attacking someone), FRIENDLY_CHAT (in place of of jabbering about rumors or the weather), DISTRESS (in place of 'Gruesome wounds! Begone fear!', etc), ALARM (in place of 'I must withdraw!'). And so on. Animals should also be able to yield and/or 'request' others to yield, based on their personality or 'goals' - a pack of wolves that want to eat you wouldn't back off if you yielded, but a territorial bear might. Some animals might make sounds when yielding (dogs might 'whine', for instance), or make sounds to REQUEST_YIELD, like growling, for animals that want you to back off but would prefer not to fight. PEACEFUL_INTERMITTENT could remain as a 'stake out territory' sound, typical of bird-calls and the like.