Marc Webb's Amazing Spider-Man films weren't based on any single comicbook line.
Webb said as much himself in an interview with Collider, conducted in 2012:
MATT GOLDBERG: Spider-Man has been around for almost 50 years, so there’s really no singular Spider-Man. From what comics did you take inspiration for your version of the character?
MARC WEBB: That’s a good question. There are different comics and different storylines, and you’re exactly right, there is 50 years worth of canon to choose from. I felt like what Sam Rami did, they started off with the Stan Lee/Steve Ditko stylized world and they were really great and generating that is kind of a genius way I think. But when I thought of Peter Parker, the questions I first asked myself were, this happened on the other movie I did and just how I read scripts in general, I want to build the character from the ground up. Who is this person, what happened to him when he was a kid, what does he like, what does he dislike. I kept on returning to this idea; this kid was left behind by his parents when he was 5 or 6 years old, that would have a huge emotional impact on anybody, that gap, that void in your life. And I kept on thinking about, well that will create a character, at least the way I interpreted it, that has a little bit of a chip on his shoulder, of this missing piece. That will define you in a very real way, so I wanted to tell a story about this kid who goes out looking for his father and finds himself, that was my access point. And in terms of finding things from the comics, obviously there’s some references to his parents and different versions of that, and I studied that a little bit. And then I liked some of the attitude in The Ultimates, and I had a conversation with Brian Bendis early on, a short one, and we talked about the relationship with Gwen and even though Gwen in my movie is a little bit more from the Amazings, I like the attitude and the physical components of Spider-Man from some of the Ultimates. So it’s an amalgam of different characters that felt interesting to me.
Director Marc Webb Talks THE AMAZING SPIDER-MAN, the Comics He Studied, Adapting Spider-Man for a Modern Context, and More
Also, in the commentary track for the The Amazing Spider-Man (2012), Webb specified a couple of things which were drawn from or inspired by the Ultimate Spider-Man comics.
Firstly, he noted that the double zeros symbol we see a few times in the movie -- in Richard Parker's notes, and in the Oscorp building -- was pulled from the Ultimate Spider-Man comics.
There's the double zeros. The double zeros are gonna play a big, important role in the movie. The double zeros were-- I think, we pulled that from some of the Ultimate Spider-Mans. Jamie Vanderbilt had seen that early on.
Marc Webb ~ The Amazing Spider-Man (2012) commentary track
Presumably it was a reference to the "00" specimen spider that bit Peter Parker in Ultimate Spider-Man Vol. 1 #1. Note that this spider was created by Oscorp, just like the spider that bit Peter in Webb's movie.
Secondly, Webb also indicated that the fight between Spider-Man and the Lizard in Peter's high school was partially inspired by a fight between Spidey and the Green Goblin in Ultimate Spider-Man.
This movie was set in high school and I wanted to create an action sequence at some point inside the high school. There was a reference to it in the Ultimates. I think the Green Goblin comes in and really terrorizes Midtown Science in one of the earlier Ultimate Spider-Mans.
Marc Webb ~ The Amazing Spider-Man (2012) commentary track
Presumably, he meant the fight that began in Ultimate Spider-Man Vol. 1 #6, concluding in the following issue.
Finally, since the previous answer draws parallels between The Amazing Spider-Man (2012) and the Earth-616 canon, I'd like to highlight some of the many ways in which Webb's films deviate from that canon:
In the Earth 616 canon, Gwen Stacy wasn't Peter's first girlfriend, and had nothing to do with Oscorp. She was just a college student, and didn't meet Peter until he started college in Amazing Spider-Man Vol. 1 #31. Peter's first girlfriend -- his only girlfriend during high school -- was Betty Brant, Jonah Jameson's secretary at the Daily Bugle. Their relationship began in Amazing Spider-Man Vol. 1 #7, and ended in Amazing Spider-Man Vol. 1 #30.
In the Earth-616 canon, Peter and Harry Osborn weren't childhood friends. They didn't meet until Peter started college in Amazing Spider-Man Vol. 1 #31.
In the Earth-616 canon, the spider that bit Peter and gave him his powers had nothing to do with Oscorp or gene-splicing. It was an ordinary spider inadvertently irradiated during a public science exhibition, as first shown in Amazing Fantasy Vol. 1 #15.
In the Earth-616 canon, Curt Connors/the Lizard had nothing to do with Oscorp or Richard Parker. And while he did become someone Spider-Man would occasionally consult on scientific matters, in comics published during the 1960s and '70s, he didn't meet plain old Peter Parker until Peter began his post-graduate studies in Spectacular Spider-Man Vol. 1 #32, published in 1979.
In the Earth-616 canon, Max Dillon/Electro had nothing to do with Oscorp. He was a lineman who worked for Con Edison, as first established in Amazing Spider-Man Vol. 1 #9.
In the Earth-616 canon, Felicia Hardy had nothing to do with Oscorp. She was a cat burglar who worked for herself, as first established in Amazing Spider-Man Vol. 1 #194.
In the Earth-616 canon, Richard Parker wasn't a scientist, and had nothing to do with Oscorp or Curt Connors. Rather, he and Mary Parker were spies working for the US government, as first established in Amazing Spider-Man Annual Vol. 1 #5. The movie version of Richard has more in common with the Ultimate Spider-Man version, who was also a scientist, rather than the Earth-616 version.
Most famously, in the Earth-616 canon, Norman Osborn -- not Harry -- was the first Green Goblin, and the one responsible for Gwen Stacy's death in Amazing Spider-Man Vol. 1 #121. Harry didn't become the Green Goblin until Amazing Spider-Man Vol. 1 #136. Also, Norman was perfectly healthy before becoming the Green Goblin, rather than dying of a hereditary illness, like he was in Webb's films.
That's not to say Webb's films didn't use anything from the Earth-616 canon; they absolutely did, Peter's mechanical web-shooters and Gwen Stacy's death being the two most prominent examples.
But I think the deviations from the Earth-616 canon are too numerous, and too great in some cases, to say that the films genuinely followed that specific canon.
They don't appear to follow any pre-existing canon particular, instead cherry picking elements from multiple continuities, and combining those with ideas the filmmakers came up with themselves.