I'm fairly sure I've seen birds inside ORD, BWI, SFO, DEN, and probably others. I think most large public spaces like shopping malls and airports get them, and I imagine they're pretty tough to completely get rid of.

I can't recall seeing any mammals loose inside airports, other than people's dogs - some people take out the leash and walk their dog like they're in a park.

While staying in the dorms at the National University of Singapore, I heard several stories of Singaporean rat agility and size, and saw a few very large rats shuffling around at night myself. Maybe there's something special about the rats in Singapore.