I am with crystalcross here in not wanting to step on toes here, but this is a very good question.
I guess it truly depends on which religion you are speaking on. Yes, many Christian based religions have taken away the souls of animals because they used to sacrifice the animals to God and felt they had to take away the soul so the sacrifice would not be murder. (I cannot really speak for some other religions because I do not know much about them.) I guess the answer would truly depend on your own belief system. =)
I personally believe in animal spirits just as I believe in animal guides. If you want to call that having a soul then by all means feel free to do so. However, I am not an animal (although perhaps I was in one of my past lives
)so I cannot really speak with any authority on this subject. I have had lots of experiences with animal spirits. Some of them beloved pets and some of them I have not known in life.
I think this is a GREAT question but perhaps one that will never have a satisfactory answer simply because each one of us will have our own opinion with no real way of ever proving one way right or wrong.