I'm a pop culture nerd and superheroes are a big thing for me. I grew up on the Superfriends, so the DC characters were always my favorites. I didn't get into Marvel until much, much later. I like my superheroes extra heroic which is why Cap was always my favorite Marvel character. He's the most like Superman in temperament. You could put Captain America in a DC comic and he'd fit right in. But they'd kick Iron Man out of the Justice League in a second.
Spider-Man was probably my first Marvel character. He used to appear in a 70's kids show called The Electric Company (starring a young Morgan Freeman as the Easy Reader).
And we watched reruns of the 60's cartoon with the catchy theme song and terrible animation. Then he had a short-lived 70's TV show. But I didn't love Spider-Man the way I did the Superfriends. His TV appearances didn't do him justice, I think.
There are two things people seem to respond to with Spider-Man. First, he's funny. People love funny. Probably more importantly, he's an Everyman. I love Superman and Cap, but you can't really relate to them. They are ideals. They can inspire you. But we're rarely going to live up to them. Spidey, on the other hand, he's got problems like we do. He's almost always in over his head.
I have argued before that Batman is the most versatile character in all of fiction. You can put Batman in any genre and it will work. I have seen Batman in space, Batman in the Old West, Batman as a vampire, Batman fighting dinosaurs... it all works. Spider-Man isn't quite as flexible, but I think he's the most versatile Marvel character out there. He holds up well in a lot of different settings.