First of all, right now, in general hunting feels much like farming random monsters in other mmos, which is not that great for a game like H&H, in my opinion. I would rather see it in mechanics that are completely different from pvp fights (or even big pve stuff like dragon fights if those ever implemented), tho devs probably going in that direction anyway.
So, animal behavior, i think it would be pretty awesome if every animal type had it's own more complicated behavior patterns as well as more advanced, and more obvious, ways of spotting player. For instance, let's say there is a rabbit, he has a 180 degree (or something) sight with fixed range, forming a cone like sight line in front of him, if player is in that zone the rabbit will spot him and will try to escape, but player can use "blind zone" to sneak on the rabbit and catch him easily. Rabbit also have a "hearing" radius with animal being the center. Rabbit can hear player walking and detect him in such matter, so player must use crawling (or something) to keep hes walking noises down (maybe stepping on an object will produce loud noise, making a set up for classic scene with branch crunch

Fox would stop all it's activities and start starring at the player, waiting for something to happen, if player starts moving towards it than fox will try to escape, if player walks away from it then, after some time, fox will return to it's unstartled state. If player is trying to attack the fox, then it will think about attacking player back or running away (say it can be based on how "menacing" player looks, guy in an steel armor with a sword looks menacing, guy in a linen shirt with a sling looks not menacing and so on).
Boar would also stare at the player (maybe will initiate a sound) but unlike the fox if a player isn't backing out slowly (or if this particular boar feels like it) it will attack. That may not only help some of the players who step into a ninja boar hiding behind an tree to potentially survive, if they know how to handle the situation, but will provide a little of a set up for funny stories "How i've met a boar and lived" as well. And, of course, if player steps right onto a boar, who wasn't able to detect him earlier, fight is most likely to occur.
Pretty much the same goes for a bear, though i'm not sure about that, cause bear plays a role of a big creepy thing in a forest you have to be afraid of, at the moment, so making bears more peaceful might be delayed till there are more scary things out there.
About animals escaping, fox will try to escape one it received significant amount of damage in fight, no matter other factors (exactly like it does now), boars and bears would do the same unless they enraged, both of them have a chance to enrage during the fight, in which case they will fight to the end (a little tweaked for how it is now).
Oh, and if animal is attacked but cannot for some time find a way to strike an attacker back it will try to escape (sup boat hunters

Generally the saddest situation in the game i've encountered so far is when animal is just starring at it's killer for half an hour doing nothing while getting sling shots from 10 mm player (actually just writing this post to kill some time while boat hunting my first bear lol). In my opinion this situation should never occur and it's a pretty important aspect of the game. I'l write some of ideas on the hunting in the following post, but i would love to see a discussion, since devs probably won't use any of those ideas, best we can do is generate something thru the discussion that would give them a worthy idea of their own. (Manny sorries for how strong my engrish is)