What year were you born if you are age 66?

It's 2008. 2008 - 66 = 1942.

If you're 66 now and you've already had your birthday this year, you were born in 1942.

If you're 66 now and you haven't yet had your birthday yet this year, you must have turned 66 during 2007, so you were born in 1941.