Exemptions for age vary greatly from place to place. Here in Washington State, I have to smog check my '79 and '83, but not the '66 or '67 -- and that varies depending whether or not one lives in a "non-compliance" area that doesn't meet clean air goals.

In Canada, I believe all cars are subject to checks regardless of age, and there's a diabolical twist: if anything is modified, the car has to pass standards for the year in which the modifications were made. This year I put a '71 motor in my '66. If I lived across the border, that car would now have to pass 2003 standards, not '66 or even '71 standards, and there's no way it would be able to.