We've got a dog (a house dog, but she roams free on our property most warm days) and 3 male cats. Our dog did good with the birds when they were out free-ranging this fall. She'd just wander around with them. Other than that, we've been lucky. The folks we got the flock from (who lived about 5miles from us) said they never had any problems either. They called the muscovies their "attack ducks" and said they and the gander kept everything at bay.
It's rather odd...the possums that did get in. I had one that curled up in the corner of my coop (we had left the pop door open late one night by mistake...till just after dark). My husband went and closed it...looked around to make sure there wasn't anything around and didn't see anything. The next morning, I went out to feed everyone, opened the coop door and glanced in the corner (where some of my birds like to lay eggs). I saw grey/black (I have barred rocks) and just walked past. It took about 20 seconds for my brain to catch up with my eyes and realize I didn't own a furry chicken. When I looked closer...possum all curled up, dead asleep. My husband and I had to wedge him out with a couple shovels and popped him with the .22. He never touched a bird (and was closed in will all of them all night). I took that as a compliment my coop was cozy. We had just finished it the week before.
The other 2 had just gotten in the run. One made a hole and one climbed the fence. We heard the gander doing his alert honk and when we went out (both times)...neither the ducks or the geese would go by the little shed. Both times, possums were eating out of the leftover feed in the dish. Never touched a bird...
We are talking about getting a new dog here, though...probably in the next month or so (a male). Our lab is getting old (she's 15 in April) and want the new one trained up before summer. We're probably gonna go with another G. Shepard (had one but had to put him down a few years back).