I'm familiar with a study that suggested dreams are used by the brain to "solidify" learned behaviors and responses. The study analyzed subjects' abilities to play Tetris (the falling blocks game, we're all familiar with it, right?) before and after periods of natural sleep. Those that had dreams featuring motifs of falling blocks scored measurably higher in Tetris performance the next day.
As a mechanism for the solidification and reinforcement of learned behavior, then, there's no reason to assume that animal brains don't also employ the same technique. As others have said, dogs appear to "chase" while sleeping, and studies confirm that animals experience sleeping brain states very similar to humans in REM sleep.
I think it's safe to say that animals dream, but that they dream about pretty much the same things they do awake, i.e. chase stuff or get chased, eat, and mate.