I somehow don't like the idea that ranger-type units start with pre-fixed animal companions. In case of rangers proper it's even more stupid, since panthers are not included as free-roaming animals. So, what I propose is to make animal companions selectable (with prerequisites; eg a city with a lion cage can build rangers with lion companions) or joinable (replacing the vile custom of sacrificing the animal to get its totem, at least for non-evil civs). A hunter could get 1 companion, a ranger - 2, and a beastmaster - 3. As for the bonuses the companions provide - that's an issue for discussion. Just stacking the totems is the obvious, though not too subtle solution.
Personally, I think that companions should give a small, flavor-like bonus, but should be able to give their promotions to their new master, a la flesh golem. Furthermore, animals should have their own set of promotions, so that a wolf with combat 1 isn't just wasted when added to a ranger with combat 1. Some promotions, like mobility, shouldn't stack, giving a different bonus (I would think of additional withdrawal chances in case of mobility). Animals should be given the ability to split from their master to conduct some missions (another tweak I offer is to grant all captured animals hidden nationality - it just seems plain logical), getting all the animal promotions of the master unit.
Also, I think animals should be able to build dens within their master's borders, and combat-trained animals should be buildable in cities (eg hunting lodge + wolf cage = combat-trained wolf). These latter might, in particular, get bronze-iron-mithril weapon bonuses (claws, teeth, spikes, whatever) or nature mana affinity (for FoL civs).
I have more ideas on the matter, and a more or less clear understanding of how to do most of these things. I'd like to know the opinion of the community, and, if anyone's interested, I'd appreciate some assistance in making this. Graphical issues, in particular, can be cumbersome.