One country that does require a notarized permission letter form parents is Mexico.
http://travel.state.gov/travel/cis_p...s/cis_970.html
Minors: Mexican law requires that any non-Mexican citizen under the age of 18 departing Mexico must carry notarized written permission from any parent or guardian not traveling with the child to or from Mexico. This permission must include the name of the parent, the name of the child, the name of anyone traveling with the child, and the notarized signature(s) of the absent parent(s). The State Department recommends that the permission should include travel dates, destinations, airlines and a brief summary of the circumstances surrounding the travel. The child must be carrying the original letter – not a facsimile or scanned copy – as well as proof of the parent/child relationship (usually a birth certificate or court document) – and an original custody decree, if applicable. Travelers should contact the Mexican Embassy or the nearest Mexican consulate for current information.