You do pony up your SSN here in the US when applying for credit. One more reason to avoid (due to fraud, identity theft, etc) the 'financing' on anything but a house, place of business, maybe a car in some cases for the average buyer.In Canada, it is illegal for anyone other than the government and your employer to ask for your SSN. When asked for ID by a store, all they get is my drivers licence number and some other piece of ID with my picture on it. If they ask for my SSN, I tell them no, they don't need it, and explain why they don't need it.
I used to live in NYC, and if I'm not mistaken, the same law applies in the U.S.