I believe so because they emit emotion. Of course, the definition of a soul varies, but mine is that they are aware and react to things that are happening around them. Even though a lot of people tend to disagree with that..
! Animals with souls? Nobody knows :)! Humans have souls though. People who would want to reject this need to explain how our brain works and how we think and feel emotion! Because if we didn't have souls we would simply be robots or mass murderers that really didn't care at all and would just kill ourselves :)
So what if we choose to believe that our pets are in heaven and then, when we get there, we find out we're wrong? While this may be painful to imagine, it's equally hard to imagine being disappointed in any way shape or form when we do get to heaven - whether we find our pets there or not. As Paul writes in 1 Corinthians 13:12: "Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know full, even as I am fully known." This text means what we don't know now, we will know in the future; and what we don't understand now, we will understand in the future. And in the end we will not be disappointed. On this particular issue, where the Bible is silent, we have the right to choose the answer that seems true to us -- that comforts and consoles us - that's based on our best efforts to reason and understand God and God's love for all creation. In the future when we enter heavens gates, God will reveal all truth.http://www.emmitsburg.net/humor/archives/insperational/pets.htm
The Bible’s creation account reads: “God went on to say: ‘Let the earth put forth living souls according to their kinds, domestic animal and moving animal and wild beast of the earth according to its kind.’” (Genesis 1:20, 24) In this passage, fish, domestic animals, and wild beasts are all referred to by the same word: “souls.” Birds and other animals are called souls at Genesis 9:10; Leviticus 11:46; and Numbers 31:28.
Applying the word “soul” to animals is very appropriate. It is in agreement with what is thought to be the basic meaning of the Hebrew term ne?phesh. This word is understood to be derived from a root meaning “to breathe.” Hence, in a literal sense, a soul is a “breather,” and animals are indeed breathers. They are living, breathing creatures.
As to their application to humans, the words ne?phesh and psykhe? are repeatedly used in such a way as to mean the entire person. The Bible’s definition of “soul” is simple and consistent. The word can refer to a human or an animal or to the life that a creature enjoys as a living soul. The Bible also states: “The soul that is sinning—it itself will die.” (Ezekiel 18:4) The soul dies when the person dies; it is not immortal.