Never
I just finished reading an article on CNN which it told a disturbing tale that brought tears to my eyes. People on the Gulf Coast who needed rescuing where being forced to leave their pets behind as there was no room in rescue boats. A kindly anesthesiologist stayed behind at one hospital to take care of a group of animals on the rooftop and one doctor euthanized some animals at the request of their owners, as they couldn't bear the thought of leaving them behind to starve - you can find the full story here, but I warn you, its hard reading.

There is no way on God's Green Earth that I would EVER abandon Molly. I love her more than words can express and I think I would let myself starve first before I'd leave her. Call me what you will, say she's just a dog, whatever. I would NOT leave her behind. Some might ask what would I do if I had the boys with us... would I still stay behind? Well hopefully Andy would be with us and I would send the children off with him. If I had the kids on my own with the dog, rather than take the children with the authorities, and leave the dog, I'd have to think about sending the children with the authorites. I would at least know they were being taken care of and could find them afterwards. It's a hard call on that as the children are not my own. I only say this because if they were my own, I would be running the risk of leaving them without a mother, and this doesn't bear thinking about. However as life stands for me now I don't have any children of my own.
It's really too hard to cotemplate no matter who the children are, letting them go without me would be stressful for them. I would just have to fight for all of us to be taken, including the dog. The children as well, would find it too traumatic to leave the pup behind.

Although they say 'never say never' and I know that the situation down south is harrowing and frightening - that people must feel so alone and frustrated with awaiting rescue, I can say with 99.9% conviction, Never. Never would I leave her behind.