That is... one minefield of a question. Depending on who's answering, you will get varying answers, all with varying tones of snobbery.
It's an ethical question, and there's no way to go about ethics without arguments. I'll save you my opinion, and just give it to you straight.
Certain religions, like Catholicism, say yes. Others, more to the tune of Protestantism, say no. Atheism, of course, will also say no. There are powerful philosophical forces driving these positions, and it's important that you learn about them on your own, and develop your own view of things.
They don't have souls that could go to Heaven, at least that's what I believe... "Animals have souls--and so do plants. Does this answer sound like something out of the New Age movement? Don't worry--it isn't. Rest assured we're not saying animals and plants have souls like ours. The soul is the principle of life. Since animals and plants are living things, they have souls, but not in the sense in which human beings have souls. Our souls are rational--theirs aren't--and ours are rational because they're spiritual, not material. Animals and plants can't do anything which transcends the limitations of matter. Although some animals seem clever, they don't actually possess conceptional intelligence. They can't, for instance, conceive of the abstract notion of justice. Animals and plants also lack a moral sense. When you scold Spot for chewing the carpet and tell him what he did was "wrong," you aren't assigning guilt of sin to him, since he can't commit a sin. (See comments...)
Yes, animals have souls. Most people would like to think that they do not, because being in a human body we tend to feel superior to all other living things on account of having more intelligence. Also, people who like the taste of animal flesh will also say that they do not have souls, but this is only because they want to eat them, and if animal did have souls and they ate them, that would surely be a sin. So make-believing that animals have no souls is an easy way to push away the guilt that they would feel if they accepted this truth.
To understand that animals have souls is very easy. You are eating. The animal is also eating. You are sleeping. The animal is also sleeping. You are having sex. The animals are also having sex. If I cut you, you bleed. If the animal is cut, he will bleed. I could go on and on. There are so many points of similarity. So to deny this one similarity, when you have so many other points of similiarity is very illogical. Every living thing has a soul. Otherwise how is it living? We are all children of God and part of His creation, therefore we should respect everyone and everything that exists. Hope this helps.
Wouldn't surprise me at all. I love dogs and I'm sure they do. No proof, just how I feel. Different people have different views, and that's fine, but what irritates me is when people give stupid reasons for not believing that animals have souls. You won't see your pets in the afterlife because they don't have speech so they can't say the "sinner's prayer." I shake my head...
It all depends on your theological beliefs. As for me all living things have a soul. I consider the soul to be the bio electrical impulses that run throughout any living thing. To put it simple a soul is the life force all living creators have. Now understand to some religions this is considered blasphemy, and even though I believe in the God of Israel and Christianity, I still fall under the title as a heretic or pagan.