About five years ago our neighbors at the top of the hill moved out and left their cats! One of them came down the hill and plunked itself on our doorstep and said "Please feed me" so we did. He turned out to be an excellent cat, I just had to put him down this week (FIV) and I'm heartbroken.
We've had our share of dumps out here, but we're on a fairly high traffic road, so its possible they choose side roads for their dumps instead.
Over the years I rescued a beagle puppy in Dec, a German shepherd, a Great Dane mix and our current dog. We also had someones Pom show up and one of the neighbors hunting beagles wandered off while they were training it.
Our current dog is an excellent LGD (I trained her, she didn't start out that way but she has excellent instincts) so I am kinda glad someone didn't want her.
Our local CL is just overrun with ads for cats, kittens and dogs people don't want. (Don't get me started on some of the reasons!) and I think a lot of the shelters are full.
Our local shelters just had "Free cat day" and the one in the city is doing buy one cat, get one free! Sad.