I don't have any pet rescue stories of my own, but I did see a fascinating one on a show once.
A woman had a large menagerie of exotic birds. One evening, her house caught fire, and her first priority was the birds (some may say she should have just rescued herself, but I'd probably try to rescue my animals too). She let a lot out before getting trapped inside the house. She was on the second story of the house when the smoke overwhelmed her and she passed out. The firefighters had no way of getting into the house from the first level and weren't sure if anyone was even inside. One of the firefighters noticed an amazon parrot squawking and pacing frantically on a tree limb outside a second story window. The firefighter brought a ladder to the window, climbed in, and rescued the woman. She would have died if not for her parrot.
Not just dogs (and cats) are heroes