Be sure to include your parents' concerns into your evaluation of future travels - doing otherwise will make you seem rebellious or immature - and be sure to follow it up with all the solid facts, research, and advice from experienced travelers/writers. The more they know you have your head on straight, the more they will trust your intuition as you fly solo.
It's also important to think about your track record and how it relates to your street smarts, travel savvy, and ability to take care of yourself. Your parents will probably always see you as a green 16 year-old, but as long as you've proven in the past you're not easily pushed over or taken advantage of, you can reason with them that you're prepared for what the world is ready to throw at you.
My parents still aren't cheerleaders for my non-professional travels, but at least they understand that I want to do it. When I had doubts about traveling around the world alone in 2008, my mom was surprisingly the voice that encouraged me to do what I want, which was against what she wanted for me. They tolerate my leisure travels these days, but my paid travel makes much more sense. It's a generational thing, as well.
Communication Makes the Difference
As a graduation present, my parents were kind enough to get me a World Edition Blackberry, which enabled constant communication via e-mail to my parents from wherever I was in the world - excluding Malawi, Cambodia, Kashmir, and Zambia, which weren't set up at the time for data usage.
While overlanding in Africa, I would wake up to the alarm on my phone and immediately receive an e-mail from my mom about the weather outside my tent flap. She was six hours behind me but still knew the weather I would experience that morning. This was certainly a way to placate her worries, because when I didn't respond to her e-mails for twelve days in a row (in Kashmir), nerves nearly sent my dad on a plane to find me.
It may be inconvenient to pay a phone bill or constantly find internet cafes to correspond from, but a quick e-mail affirming your happiness and safety are great ways to facilitate your parents' sleeping patterns.
A Mother's Perspective
It seemed only fitting to ask my mother her opinion on my travels, safety, and her feelings toward my independent travel lifestyle.
The summer before I entered sixth grade, I asked my parents if I could attend a military camp an hour north of our town, a camp my brother attended the previous two summers. Though his camp sessions were only two weeks at a time, I decided I wanted to experience the six week, intensive summer camp, which involved three different sessions of learning new skills, bunking with fifteen other girls in a log cabin, and all things military: general inspections, personal inspections, marching, etc. I went to this camp knowing no one previously.
Most ten year-olds don't normally ask for such experiences, and my mom noted this as major characteristic difference between myself and my peers. My independence was obvious at a young age.