Jurgens, though I guess he had a significant (if short) run on Spider-Ben.
Walt Simonson used Peter in that Fantastic Four story, but I don't think he did much with him otherwise. Louise Simonson was responsible for some significant stories in the run-up to the marriage era.
Petrus Maria Johannaque sunt nubendi
So I went comixology and got a few issues and yes! I loved the four issues I got. I was lucky in that I picked out 82-85 and it was a complete story with him teaming up with Black Widow and Nick Fury and Master of Kong Fu. Really enjoyable story.
I really want that Red Sonja one. I love Red Sonja comics and would like to see the whole connection with MJ there..
John Byrne was part of the team that relaunched Amazing Spider-man with volume 2. I don't remember if he just did art or if he was involved in plotting as well.
If you can find the Spider-Man/Red Sonja miniseries crossover in TPB, the MTU issue is included there as well.
Also, for those mentioning Garth Ennis, he did do the first three issues of Spider-Man: Tangled Web that introduced an even worse bully than Flash Thompson ever was, Carl King, as a new foe called the Thousand, made up of a swarm of a thousand spiders united by King's diabolically twisted psyche after King ate the spider that bit Peter Parker in hopes of becoming spider-powered himself. For what it was worth, Ennis did do a pretty solid portrayal of Peter's character, at least from what I remember reading.
The spider is always on the hunt.
His Sensational run is really good and does an excellent job defining Ben Reilly's character. I was stunned to learn years after reading that he hated Ben.
Neither of my two answers are natural fits for the character, but I would love to see Grant Morrison or Neil Gaiman write Spidey. Both are probably still possible.
Quite a bit - my understanding is that he ghost-wrote the Spider-Man newspaper strip for years for Stan Lee.
As far as big-name Marvel creators who never really wrote Spider-Man, Steve Englehart is a big one. Given that he wrote for basically every other big name at the company, maybe he just didn't really have a feel for the character.
I really enjoyed Englehart's West Coast Avengers. I never got into the main Avengers book but that one I did.