Do you believe that your 'animal companions' dream when they sleep?!

Do you believe that your 'animal companions' dream when they sleep?

(a.k.a. pets...just being PC :-) )
When our dog is sleeping, I swear he's dreaming about chasing something....his legs go nuts, like he's running. And he barks in his sleep!!
I've read articles that basically say pets don't have the mental capabilities to form thoughts, so therefore they can't dream. I say that's not true! What do you think?

3 days ago
GREAT answers!! :-) I'm a firm believer that pets have an incredible amount of intelligence! (I agree...seems like they have more than some people I know!)

I think that they do dream ..my 2 dogs do the very same thing. I really think people under estimate animals and what they think or know. It's arrogance on humans part to believe we're the only ones on this earth that can put 2 and 2 together. My dogs both have done things I've never taught them and I've had both since they were pups. If they're so stupid as some would have us believe where did it come from....from thought and intelligence I say.