As long as you're not a literal child, no age is off-limits for independent travel! Just do it as much as you can and as soon and often as possible. The obvious advantages of being a young traveler is that you are less likely to be saddled with serious health problems and demanding life responsibilities (which can lead to low energy and a cranky, jaded disposition).
So, of course I encourage all young people to travel far and wide, ASAP and to the max. Take advantage of your high energy levels and relatively low responsibility load -- travel (like just about everything else) is more enjoyable if you're not already physically exhausted and psychologically preoccupied.
Still, it's never too late to start traveling! I'll admit that traveling in my twenties was a bit easier / simpler than doing it in my forties. Today, I've got a "writer's back" -- meaning that my whole torso is perpetually stiff, bent out of shape and on fire. Proper nutrition, good sleep and regular hydration are disciplines I can no longer ignore if I want to be functional. I now get nervous about the availability of bathrooms, because my formerly iron bladder has been replaced with a loosely-stitched quilt made out of tattered burlap sacks. It's also harder for me to get relaxed, excited, surprised or wowed by something anymore. These were all non-issues in my twenties and thirties when I seemingly had infinite social energy, didn't need to rest ever and got all my nutrition from potato chips, beef jerky, beer and cigarettes...
But so what? As we age, we become mindful of new challenges and we handle them; we adjust our travel styles and we keep going. And even as I grow more experienced and less easy to impress with age, traveling never fails to awaken the wide-eyed child in me.
No matter how long you've been around and how much you've seen, if you give yourself the time, the space and the autonomy to “hit the road” on your own terms, you will definitely discover new wonders – in the world and within yourself – that won't leave you unaffected.