Spoilers for the Ultimate Spider-Man Death of Spider-Man arc.
Despite being first exposed to the Web Head on Spider-Man and His Amazing Friends, my definitive Spider-Man was the one from the comics in the 90's. That's the married Peter Parker, not Ben Reilly (although I love Ben to death). I hated One More Day because it was such a horrible way to change the character, and while the Brand New Day stories did get better (mostly because they stopped interfering with the dang book with all these events and crap!), I felt a disconnect and had to drop the book.
I never stopped reading Ultimate Spider-Man, and I have every issue of the original run, 160+ and 3 annuals from the last ten years or so. That Peter Parker was radically different, still in high school and given a more modern story (one the movies and the last two animated series draw heavily upon). I love Bendis' Ultimate Spider-Man, despite not being my definitive Spider-Man, and while I was spoiled about it months ago because I'm so slow, I was still absolutely shocked Peter was killed and replaced by a new Spider-Man. And saddened, because that's how much impact the character had on me.
The bottom line is, as I've always said, Spider-Man is such a unique character because just look at what superheroes were like when he hit the scene in the 60's. He proved that teenagers don't have to be sidekicks, they can be heroes in their own right. And with that, of course, comes teen angst. Feeling responsible for the death of his uncle, taking care of his sickly aunt, job problems, school problems, girl problems. Spider-Man OWNS that, I don't care what anyone says about any teenage hero, they owe it to Spider-Man.
HOWEVER Spider-Man shouldn't be all angst all the time. I mean, the guy's a cutup. His rapid-fire jokes are another thing that makes him who he is. One of my absolute favorite comics of all time was a (Spectacular, I think? by Paul Jenkins) that was a flashback to Peter's childhood with Uncle Ben that wasn't filled with angst because it was all about how Ben taught him to laugh.
And that's what Spider-Man is to me. He's an underdog, both in and out of costume, fighting against the Parker Luck, but at the same time, that stuff doesn't beat him down. He can laugh it off and continue to do the right thing, the responsible thing, and still be optimistic. A quick rundown of how well I think they've handled this balance in TV and movies:
Spider-Man and His Amazing Friends - Brought the funny, but lost a lot of the Peter Parker stuff. He was in college, which was fine, but having Angelica and Bobby as his superpowered entourage was...strange.
Spider-Man: The Animated Series - I loved the more responsible, smart Peter Parker who threw wisecracks around and was mature enough to actually get married. Closest there is to my definitive Peter Parker.
Spider-Man Unlimited - An interesting twist having Spider-Man go off into space to take care of Venom and Carnage, who he considered were his problems, but the Peter Parker side of this wasn't interesting. His love interests didn't make any sense, and his photographer job wasn't anything new.
Sam Raimi Spider-Man Movies - WAY too angsty and not nearly funny enough.
Spider-Man: The New Animated Series - Basically the same as the movies, only he was funnier (thanks to Neil Patrick Harris), but his girl problems were more tiresome.
Spectacular Spider-Man - A definite lack of maturity on his part, which is probably because he's at least a few years younger than the others, and his relationship with Gwen was getting to be tiresome, at least his Spider-Man persona did a good job of showing how seriously he takes his responsibilities. The humor worked well too.
Ultimate Spider-Man - At least where it stands right now, it goes too far in the opposite direction as the Raimi movies. WAY too much goofball stuff and his life as Peter Parker seems negligible. Even worse than Spider-Man and his Amazing Friends because this show seems to be saying Harry and MJ are important and yet constantly show Peter/Spidey spending time with the other heroes, both in costume and out. The show's funny, and Spider-Man does get his comeuppance when he does something irresponsible, but he just feels like too much of a screw-up and an idiot at this point.
Amazing Spider-Man - There's a good chance I won't see it in theatres. Just from what I've seen, it's a bit too...dark.