Neuromancer was written in 1983 (the original edition has the first digital art book cover, by Rick Berry) and is set sometime in our future when flights to orbitals are routine. At the same time, there's pay phones. There was a fair amount of bad-guessing future in this, but the story mainly carried anyway. Our protagonist, Case, is a guy who breaks digitally into banks and companies. He defrauded his bosses and they screwed his brain so he couldn't do it anymore. We meet him in Chiba City in the nightlife. He's acquired by a new boss who gives him new organs, including a brain that will hack, and for part of the book, he doesn't even know what the job is. It becomes more complicated -- who's cheating who, who's lying, etc. -- and more violent.
It happened that james_nicoll had a post on Neuromancer last Sunday, and in the process, carloshasanax and Doug M. who posts anonymously mentioned that the book follows Dante's Inferno. Now, I knew the idea of Inferno, but not the exact form, so I looked it up in Wikipedia, and I must say, they seem to have a point. I found more and more correspondence between the books.
I don't think I'll read more Gibson, it's still hard to read for me, but I think if I'd managed to read it back in 1983, I might have felt it was the classic so many others do.