I think that is not a black and white question. I believe that all life 'energy' is connected and interdependent. I firmly believe there is more than just this life. If that is the case, then yes, animals have souls.
However, I'm not terribly interested in meeting all the flies, spiders and various insects I've squished over the years!
Yeah I would be in BIG trouble with the spider spirits. Seriously-excellent question that may turn into a religious debate! Jax08 put it very well. I do believe we see those in our lives again after we die.
You can look into your pet's eyes and know they have a soul. I seriously pray that I never have to look into any of the eight eyes a spider has to see if it has a soul. But I think I'll pretend they don't.