What is the most important lesson that Ponyboy learns in The Outsiders?

Ponyboy learns there are more similarities among young people than differences. He also learns there is goodness in others and, most importantly, that violence serves no positive purpose.

When Ponyboy talks to Cherry in Chapter 3, he learns the Socs have problems, too, although they differ from those of the Greasers. Interestingly, Cherry seems to understand Ponyboy: 

"You read a lot, don't you, Ponyboy?" Cherry asked. 

I was startled. "Yeah. Why?" 

She kind of shrugged. "I could just tell. I'll bet you watch sunsets, too." She was quiet for a minute after I nodded. "I used to watch them, too, before I got so busy. . . "

From Cherry and others, Ponyboy learns there is still goodness in the world. Yet, there is also peer pressure for both gangs. Like the Greasers, the Socs have parents who neglect them, although for different reasons.

With the knowledge that he gains from his experiences, Ponyboy learns the important lesson that violence serves no positive purpose. This idea is expressed in Chapter 7 when a Mustang pulls up as Two-Bit and Ponyboy stop at the Tasty Freeze to relax and have Cokes. Randy and a tall boy who nearly drowned Ponyboy are inside; Randy asks Ponyboy to get into the Mustang and talk with him. In the course of their conversation, Randy praises Ponyboy for his courageous act of saving the children in the church fire. After saying a few other things, Randy tells Ponyboy that he is not going to participate in the rumble between their gangs:

You can't win, even if you whip us. You'll still be where you were before—at the bottom. And we'll still be the lucky ones with all the breaks. So it doesn't do any good, the fighting and the killing (Chapter 7).

Ponyboy knows Randy is right. Nothing positive comes of violence. Instead, he has lost boys that he has loved to it. This is his most important lesson.

As a summation of his experiences and thoughts, Ponyboy arrives at the realization that "[N]othing gold can stay." Words are much more effective than actions; therefore, he writes with the hope that what is "gold" in people can "stay" as it is recorded.