[eemy]

I'll refrain from listing for Canada, as any building in Canada has a much stronger association to the city than country for me, even the Parliament Buildings. Put it up to rampant regionalism or something like that. I've always felt that Canada has adopted natural features as the preeminent symbols of our country anyway.

For the US:
Statue of Liberty
White House
US Capital
Gateway Arch
Kennedy Space Centre
Mount Rushmore
Possibly Empire State Building, though I think of it more as a symbol of New York than the US.