He gave a voice to teens when it seemed like they didn't have one. He made it acceptable for teens to have feelings, deep feelings of angst, anger, sadness etc. Being a teen wasn't just a transitional phase and he embodied that in Rebel.
I think he also showed it's ok to be different. He wanted to try everything and be the best he could be. He showed that once you obtain success to reach for more. He is still influencing people today with that mentality, I for example am not ok anymore just being the "typical Army wife and stay at home mom" Why not broaden my horizons and learn new things.
That's my 2 cents.