I only took one international trip without at least one of my parents before the age of 18, and that was to Mexico at 16. It was a resort destination, so the Mexicans could care less. I can't even remember if I had a permission letter from my parents, though I do know that at least one of my parents came to the airport and the gate before I left (was long before 9/11).
The only issue I had was with the Customs idiot making the presumption that since I was 16 and traveling alone from Mexico, I would of course have a small amount of marijuana (likely for me and my friends to get stoned and not hurt anyone), so he ransacked my bags and even jacket. Guess he was looking for his "big catch." When he didn't find anything, I asked why he had singled me out and he actually admitted it. I told him I was insulted, that I didn't even drink alcohol and that he was a jerk for making that presumption. I found his supervisor and made the complaint. Started early I guess