Peter Parker represents the everyman in the world of comics. While characters like Batman are rich and Superman is just an alien, Peter Parker started off as a teenager who got bullied, wasn't very popular, and struggled with money. He's also incredibly anti-social.
Yet, he almost becomes the villain of the story once he gets his powers. He lets a burglar get away just because he wants fame and fortune. He grew selfish. Yet, his crucial mistake led him to take his selfishness to another path: his selfish ambition to keep others safe.
This is what I find amazing about Spider-Man. Even he has moments where he is greedy, cheats, and abandons friends (like Harry, for example). His Spider-Man persona gets in the way of normal life. He still ends up being a good person in the end despite not having good luck or making really bad decisions. We still root for him when he decides to try and get revenge despite it being wrong. Why? Because he's like us. He's the virtual representation of how a normal person would act having super powers.
Yet there's more to him than that. He has high morals, and is constantly learning from his mistakes. One of his key features is his overcoming will. Even though he's very human like the rest of us, he still is a super-human, and shows the potential of what a super hero could realistically be.
He's just a brilliant main character, something you don't always see in literature nowadays.