For a member of a fairly hardened and violent gang, Johnny Cade is generally quiet and passive. He is the son of an abusive home; therefore, he doesn't spend much time at home. His "family" is the Greasers, and the Greasers know this. They watch over him like a lost puppy or a vulnerable little brother.
"a little dark puppy that has been kicked too many times and is lost in a crowd of strangers"
He tends to be a bit skittish as a result of his beating at the hands of the Socs. All of the above contribute to him seeing himself as somewhat worthless. He doesn't outright say that, but it's clear from his actions that he is willing to throw his life on the line for others. That's not because he's very altruistic. It's because he thinks his life is worth less than the person next to him. It's why he runs back to save the kids. It's probably why he's willing to kill Bob to save Ponyboy.
Despite all of the negative that I just listed, Johnny is not spineless. He practically worships the ground that Dally walks on, but he stands up to Dally when he is pestering Cherry and Marcia. Considering his situation, I'm always surprised at how accurate Johnny's moral compass is.