In Canada you can refuse to give someone your SIN for non-government purposes ... in theory. I was once refused an apartment sublet once when I did this. I had to come back with evidence that the landlord had no legal right to collect the SIN. That and the strong implication I was capable and willing to file a complaint.

People use all sorts of zany things to try to prove identity. I think public education is the first line of defence against the misuse of things like SSN/SIN.