I'm a Celtic Reconstructionist, and my view of spirituality is both polytheistic and animist at heart. I do quite a bit a work with animal spirits, as well as ancestors. I don't see them as having been "totems" in a strict sense of being representative of a particular tribe, group, or family, but more as in spirit presences who sometimes elect to assist a person either for a particular incident or through part/the whole of one's lifetime. Certain animal spirits bring different qualities into a person's life, or may express qualities a person has. The salmon, for instance, being a bringer of wisdom, while the crow or raven is a battlefield guardian and shapeshifter.
I've done a good bit of work and study in Siberian shamanism as well, specifically in the forms practiced by the Ulchi tribe of Southern Siberia. Among these people, animal spirits are regarded as capable of being both helpers to a shaman, and of standing in opposition to their work. It isn't that a particular spirit is regarded as "good" or "bad," but simply that the goals of such spirits are not those of humans. The shaman makes offerings to the spirits, sings to them, asks for their aid, and sometimes directs them. Helping spirits may be mischievous and play tricks on the shaman they aid, and so caution and good relationships with one's spirits are paramount. The spirits who help a shaman may or may not get along together, and so not all spirits may be called upon when the shaman is doing his or her work. One can offend spirits by not making proper offerings, by insulting them verbally or by deed, or by violating prescribed social behaviors, such as speaking of spirit-things outside one's house or shelter.
In much of modern NeoPagan culture, when people speak of identifying with a particular animal spirit, it's usually because they feel they embody or would like to embody the qualities of that animal -- the bear's strength or reputation as a healer, the eagle's sight, the wolf's leadership, or the coyote's joyful trickster nature. I suspect there's some element of this within tribal cultures (feelings of affinity), but so often I see people who choose their "totem" or "spirit guide" out of a deck of cards by random draw, or have a Priest/ess tell them who their "spirit guide" is, or read a description in an occult book about animal spirits and pick one from a list. My personal feeling is that such relationships can't be indicated or mediated by a deck of cards, by what we desire, or by another person. I feel that when a spirit comes to a person, it will be through dreams, or through significant events in waking life; that such an event will be powerful and have the force of a sign or omen. It's not just sighting an animal in the woods, for instance, but an encounter that leaves one breathless and full of a feeling of great power and awe. Such encounters are often only the beginning of a series of encounters with that animal on both the physical and dream/spirit realms.
I believe that many people have natural talents for soothing and communicating with animals, but that this power doesn't necessarily indicate a spirit connection with a particular species. Dogs tend to like me very much, but none of the spirits that work with me regularly are canine, for instance. Those creatures that come to me in dreams, that speak to me, and that advise me are of other species.
Questions to ask oneself in regard to these encounters:
Do the dreams or visions carry symbolic significance?
Do the waking-world incidents carry a sense of the numinous?
Do the creatures encountered appear to be teaching something or showing you something about yourself or the world around you?
Are the creatures behaving in a "natural" way for that time and place, or is there something unusual or "unnatural" about the event?
I believe that most people have some connection to animal spirits of different kinds. I believe that we need to listen and observe carefully when we feel that there is some larger spiritual component to our interactions with the creatures in our daily lives. I believe that dreams and visionary experiences must be sorted through and interpreted before we can draw any conclusions about the nature of their significance to us; that some dreams are simply a way of our subconscious relaxing, and that other dreams are an interaction with the life of spirit.
It's up to us what we do with the information we receive, and how we interact with any spirit (animal or otherwise) that presents itself to us as a teacher. Use caution -- in the spirit world as in waking life, not all is what it seems.