[Background: I started my first business at 12, 3x founder by time I was 22. Named by White House as one of the top US entrepreneurs under 30.]
Young entrepreneurs can succeed, just like older ones can. Younger founders have certain pluses that older ones don't, and vice versa. One group is not inherently better than the other. Example: youth has fresher eyes to innovate, but lacks scar tissue that comes with experience.
However, being young does have its advantages. Many of them have been covered in these answers. I'd boil it down to: higher risk tolerance, less preconceived notions that constrain innovation, and stubbornness.
I often advise young entrepreneurs to "Be young, do stupid." I wrote a blog post about a group of aspiring young student-entrepreneurs who paid out of their own pocket to visit Silicon Valley from Singapore: http://blog.isocket.com/2010/07/be-young-do-stupid-aspiring-entrepreneurs-are-awesome/
On the flip side, being a young entrepreneur is disproportionately difficult. One of the reasons is what I call the Lemonade Stand Syndrome - where people pat you on the head and give you a quarter because they think it's cute, regardless of how well your business is doing. They treat you differently, even though most of them don't intend to.
For example, our company culture is to treat people as old friends. One habit of which is in our phone calls or meetings I will often call people "man", "brother", "dude", etc. I was once criticized by a VC for being immature because I said "Take care brother!" when we were leaving our meeting. Were I 50 years old, I doubt he would have been calling me immature. (Yes, I will still call people dude when I'm 50!)
Another example: In my teens I once brokered a legally-creative real estate deal. It was totally legal, but unusually crafty. I hired an attorney to close the deal. My own attorney called the other party and said "You should walk away from this, this is just a kid and there's no way this deal is kosher." Were I 50 years old, I doubt he would have thought the same way. I fired that attorney, got the deal validated elsewhere and it went through, and I netted $50k in a few weeks.