> Liz Allan - revealed to be the Molten Man's step-sister in the 1970s, later married Harry Osborn (Green Goblin II), bore his son, and between the Clone Saga and BND was Norman Osborn's (Green Goblin I) daughter-in-law.
Liz graduated to being an active co-conspirator with Norman Osborn in the final arc of Superior Spider-Man, making her essentially a super-villain's henchperson.
> Flash Thompson - became the new Venom after OMD.
Even before that, he had a stint being framed as the first Hobgoblin, dated Felicia Hardy without ever finding out she was the Black Cat, and was left in a vegetative state for a time after Norman Osborn targeted him to get at Peter
> Sha Shan - I vaguely recall that her grandfather was some kind of priest/mage who was somehow connected to Dr. Strange. She also used to be the villainess Sister Sun, partnered with a certain Brother Power.
In fairness to Sha Shan, she actually started out "superish" and was "normalized." Her first appearances revealed that her father was a mystic, and her second appearance had her as Sister Sun. After that, though, she became a basically normal person and that stuff was never again mentioned.
> Aunt May (although she used to be Doc Ock's fiancee)
Also, she's twice been held hostage by the Green Goblin/Norman Osborn and had her death faked by him once, a status which lasted for months even in-universe
> Joe Robertson and his family
Joe turned out to have a past with the criminal Tombstone and spent some time in prison for failing to report Tombstone's murders out of fear; pardoned eventually.
> Glory Grant
Dated one of the Lobo Brothers and accidentally shot and killed him while trying to kill Spider-Man
> Ashley Kafka?
Became head of an asylum full of superpowered nutcases; murdered by Massacre during Superior Spider-Man
It's worth noting that Liz Allan's relationship to the Molten Man, John Jameson's turn as Man-Wolf, Aunt May nearly marrying Doc Ock, Joe Robertson's past with Tombstone, Glory Grant's relationship with one of the Lobos, and Professor Warren becoming the Jackal were all Gerry Conway plots. Stan may have tied some of the villains up with Spidey's supporting cast, but Conway was arguably the guy who made it almost mandatory that no one could stay "normal" for too long.
He also did a story where Mary Jane was targeted by the third Vulture, the mutated Clifton Shallot, because she bore an almost exact resemblance to someone who knew his secret. And he did the story where Flash Thompson's entire apartment building is being manipulated by the Mindworm.
Some further additions:
Stacy family: Arthur Stacy turned out to be tangled up with Ranger and the alien Senator Ward; his son Phil joined anti-mutant group the Sons of Humanity and wound up fleeing assassins like the Shocker when he turned on them
Jacob Conover - went from a minor Daily Bugle reporter most notable for writing up the news article in "The KId Who Collected Spider-Man" to being one of the many incarnations of the Rose
Joy Mercado -- stayed mostly normal, recently turned up after years of absence as a blogger in an issue of the Warren Ellis Moon Knight
Kate Cushing -- had a sister who joined a cult, but otherwise stayed quite normal despite working for both Jonah and Thomas "puma" Fireheart
Nathan Lubensky -- turned out to have a gambling problem that got him targeted by the mob over and over; died of a heart attack in a confrontation with the Vulture
Aunt May's boarders -- had pretty "grounded" plotlines, actually; even the one action-oriented storyline was basically a "ripped from he headlines" take on the Bernard Goetz incident
Steve Hopkins - Peter's closest friend as a grad student; vanished after Peter quite school
Phillip Chang -- introduced as a character tangled up with the White Dragon, but was soon "normalized" as Peter's grad school buddy; vanished with the other TAs
Roger Hochberg -- Peter's lab partner; vanished like the other TAs
Chip something-or-other -- Peter's colleague during his second stint in grad school; killed by Carnage during the latter's initial rampage