Listed below are just a handful of what I consider to be the definitive classic Spider-man stories. This includes any story from the so-called "real" Marvel Universe, a.k.a the Earth-616 Universe. This does not include any "Ultimate" stories, alternate-Spider-men etc. (sorry Miles). This is just an excuse for me to geek out on one some of my favorites.
Spider-man: Visionaries by John Romita Sr. - This trade paperback collection features several stories, drawn and handpicked by arguably (he may be tied with Steve Ditko) the greatest Spidey artist himself, John Romita Sr. Featuring iconic moments from Spidey's classic era, including the first appearance of Mary Jane Watson, the "Spider-man No More" story, the first meeting between Spider-man and Doctor Strange and many more. All stories written by "The Man" himself, Stan Lee!
Spider-man: Sinister Six - The trade paperback of this story reprints the first appearance of The Sinister Six in Spidey's first annual (The Amazing Spider-Man Annual #1 (January 1964) and then continues with The Return of the Sinister Six, published nearly 30 years later in The Amazing Spider-Man #334–339. The original story by Lee and Ditko features Spidey's greatest rogues (Dock Ock, Electro, Kraven the Hunter, Mysterio, the Sandman, and the Vulture) teaming up to take revenge on our beloved wall-crawler. Through some clever wit and quick thinking, Spidey brings down their scheme. It's follow-up tale, under the team of David Michelinie and Erik Larson, brings in a rebranded Six (Kraven died and was replaced by Hobgoblin). The story puts Spidey into a compromising situation, while also juggling his shaky relationship with MJ, at this point his wife. It's one of Michelinie's best stories.
Spider-man: Death of the Stacys - This is the set of twin-stories that most people hail as the "greatest Spider-man saga ever told." It truly is Spider-man's turning point! If you want to understand the character of Spider-man, this is the one story you should read. The death of Captain Stacy was one the most intense deaths for Peter after Uncle Ben. To then compound that with the death of the teenager's first love, Captain Stacy's daughter, Gwen, ramps up the pathos and drama to the Nth degree. It cements both Doc Ock and the original Green Goblin (Norman Osborn) as Peter Parker's two greatest nemeses. Gwen's death is Spider-man's moment of realization that his life will never really be without great conflict. The Captain Stacy story was written by Stan Lee and drawn by Romita Sr. Gwen's death was written by Gerry Conway and cements him as one of the greatest Spider-man writers of all time. Art was done by Gil Kane (probably the 3rd greatest Spidey artist after Ditko-Romita Sr.)
Spider-man: Return of the Burglar - Written by Marv Wolfman with art by Keith Pollard, Al Milgrom, and Sal Buscema, the story told in Amazing Spider-man #193-200 brings Peter Parker full circle, back to the day he caught the burglar that killed Uncle Ben, back to his earliest time wearing the webbed mask. It features a somewhat odd Kingpin interlude, the first appearance of The Black Cat and then it all evolves into a decent Mysterio story. There's a reasonable amount of repetition and it does drag a little though compared with some of the earlier stories it's a lot tauter. Pete is really put through the paces here and, ultimately learns an important lesson, that you can't really ever escape your past.
Spider-man: Blue - This story is the best of the "Marvel Color Books", written by Jeph Loeb with art by Tim Sale. It is a retelling of Peter Parker's reaction and response to The Green Goblin's murder of Gwen Stacy. It's a touching romantic tale. Well-paced and heartfelt, it balances action and drama carefully and helps Peter resolve the loss of his first love.
Spider-man Vs Doctor Octopus - This is a trade paperback reprinting the best Spidey/Ock encounters ever. It's another cheat because it features multiple stories. Featured are Amazing Spider-Man # 3 (Doc Ock's first appearance), 54-56 (reprinted as MARVEL TALES) and 130-131 and Annual 15. It was collected in conjunction with the Spider-man 2 movie. This book gives you every major important Doctor Octopus story from the silver and bronze age. After the origin story (one of the best Spider-man stories by Stan Lee) Ock swindles May Parker into almost marrying him (the start of the legendary and wonderful Octopus/Hammerhead war by Conway/Romita) and convinces an amnesia-ridden Spider-man to work for him (this story was adapted as an episode of Spider-man: The Animated Series in the 1990's). Plus: the debut of the short lived and comical Spider-mobile. Great work by the legendary John Romita Sr. on art and wonderful writing by Stan Lee and Gerry Conway. And then there is the annual... Annual #15 is one of my favorite Spider-man stories of all time. It's Spider-man vs The Punisher and Doc Ock. This was written by the delightful Denny O'neil and remains one of the few Frank Miller drawn Spider-man stories.
Amazing Spider-man #241: "In the Beginning"- Published in 1983, this story reveals the origin of Adrian Toomes, The Vulture, one of Spidey's earliest and greatest villains. It's a compelling origin and culminates in a very entertaining battle between Spider-man and Vulture. It's beautiful to look at to, considering John Romita Jr. drew the story. It also happens to be written by one of the greatest Spidey scribes ever, Roger Stern.
Spider-man: The Origin of The Hobgoblin - Probably the greatest mystery story ever published featuring the Wall-Crawler, this one introduces one of Spidey's most memorable foes, The Hobgoblin. Spidey fans in the early 80's had been begging to see the return of Norman Osborn as The Green Goblin. Roger Stern and John Romita Jr. gave them something new and different. A new "Goblin" who steals all of Norman's tech. This is one of the greatest Spidey stories of the 1980's and, the only trouble with it is, you don't find out the actual identity of this new Goblin, until much later, and under a new writer. Stern would return later to pen a story that features the true identity of HobgoblinAmazing Spider-Man #248: "The Kid Who Collects Spider-man"- Published in 1984, it's yet another Roger Stern story, this time with art by Ron Frenz and inks by Terry Austin, in which Timmy Harrison, a terminally ill child and Spider-man's biggest fan, meets Spidey and reminds Spider-man why what he does is so important.