Peter Parker's issues in the comics, outside of Flash, are mostly from his consistent and constant failure to balance his life as Spider-Man with his life as Peter Parker. Spider-Man could solve Peter's problems, but to do so would negate the lesson he learned at Uncle Ben's death. So, Spider-Man is a selfless hero, but that same selflessness causes his life as Parker to suffer.
That's it. That's the core of Spider-Man.
Let's look at early Spider-Man (IMAGE HEAVY, click the images to enlarge), and thus early Peter Parker.
Amazing #1: Back to Peter is his day-to-day. Bullying? Nah, he opts out on his own. Why? So he can make some money as Spider-Man. (Yep, he doesn't give that up immediately after Ben dies.) In fact, if you look at all the early Amazing issues, Parker is a part of the Flash clique, except he has to dip constantly and Flash always gives him a hard time.
In two issues, Parker has a job at the Bugle as Spider-Man photographer - remember he's in high school - and as the top scientist in his class, professors are always asking him to join them. And what? He gives Flash as much as he gets? Shock!
What about that blonde girl? Liz Allen! Oh wait! Let's jump to Amazing #4. He has a date with her. He blows it because of Spider-Man stuff, but again, he has a date with Liz Allen! Even at the end when Flash is throwing shade, Liz tells him to stop.
Amazing #7: Here's Peter taking a break from highschool and Spider-Man problems to mack on Betty Brant, the Daily Bugle's secretary.
In ASM (the film), people got in on the scene where Peter with power publicly takes on Flash, except, you know that happened in the comics. Again, this is issue #8, where Peter is openly fighting with and making fun of, Flash Thompson.
Flash even starts to soften (Issue #9), but alas Peter's too busy thinking about other stuff and he gives him the cold shoulder. Same issue, Pete's already A) hot, because Flash crushed his glasses and B) in a relationship with Betty.
Liz and Flash comes visit his aunt in the goddamn hospital!
Issue #12: Liz steps up again to make a play. Peter shoots her down, because he's dating Betty.
This is 12 issues in, if you don't count Amazing Fantasy. By #15 he has two women fighting over him almost full time (Liz and Betty hate each other). That's how long Peter Parker was a sad sack in the way that some see him. It's a flanderization, pure and simple. People have this conception of Spider-Man that simply doesn't match up to anything and Raimi's films were a part of that.