SassyC, I had a cat and dog just like that!  My cat Hobbes would "beat up" my dog, or pounce on her and attack.  It was good entertainment!
Our only "official" pet now is our dog.  She's half husky & half chow, and has a boy name thanks to DH.  We've had her for over 10 years, so she's getting old.
Unofficially, I've got a bunch of squirrels, but my kids think there's just 2 (since that's how many we see at a time).  They're named Chocolate and Vanilla.  We've got a woodpecker working on the telephone pole, moose eating my garden spinach, ducks and 2 swans we pass when we go to and from home, horses in all directions but we don't actually own any (just lots of our neighbors do), Sniffer - a neighbor dog who comes to visit our dog alot and sometimes sleeps on our porch - the kids named him this after what he does  , lots of red-breasted robins, ravens, chicadees, and who knows what other kinds of birds are out there.  I just know they're loud when I'm trying to sleep in the morning.