Spider-Man

Spider-Man or Spiderman (PROSE: Only Human) was a fictional superhero with the ability to scale buildings by crawling along their sides, not unlike a spider. (PROSE: To the Slaughter) The Seventh Doctor once stated that "with great power, comes great responsibility," a quote that he thought came from Marvel Comics. (PROSE: Timewyrm: Genesys)

Completing the argument that Jason was making about the immortality of fictional characters, the Seventh Doctor said that if Spider-Man aged, he would be collecting his pension. (PROSE: Conundrum) During an attack on the Fifth Doctor's TARDIS, a Spider-Man cartoon show was playing on the scanner screen, shortly before the screen's destruction. (COMIC: The Stockbridge Horror)

In 1972, Maxwell Collins had a shirt with Spider-Man on it. (COMIC: The Pestilent Heart)

In 1977, Billy Wilkins, finding the Eighth Doctor's methods of dealing with the Morg ineffectual, claimed that Spider-Man would've finished it off by now. (COMIC: Doctor Who and the Nightmare Game)

There was at least one film about Spiderman, though its title wasn't clear. Das watched the film and thought the character Spiderman was real. Jack Harkness told Das that Spiderman was a fictional character in the movie and was played by an actor. (PROSE: Only Human)

Other references
When Clyde Langer accidentally walked into a spider's web in one of Ashen Hill Manor's secret passages Rani Chandra laughed and said "Very spider-man!" (TV: The Eternity Trap)

Comics

 * Spider-Man was created by Stan Lee and Steve Ditko and debuted in, with Andy Yanchus colouring the comic. The quote about power and responsibility comes from this first story. The first of Dr Who's Time Tales was reprinted from this same issue.

TV series

 * The can be recognised by the quoted line from its theme song. Technically, it isn't possible to tell in The Stockbridge Horror whether this is a cartoon with a song or if someone is warning him about the coming of the Spider-Man.

Parallel universes

 * Death's Head's frequent travels between universes have placed him in at least two parallel universes where Peter Parker (Spider-Man) is a real individual. By travelling back in time, he would've been able to meet the Spider-Man of Primax 185.12 Gamma (Earth 120185), Marvel UK's Transformers universe, and the of, the mainstream Marvel Comics universe.

Films

 * One idea for The Lazarus Experiment was a mad scientist working on developing invulnerable synthetic skin; it was dropped because Davies feared that this might be part of the plot of the movie Spider-Man 3, which was due for release around the same time that Greenhorn's episode would likely air.
 * Andrew Garfield played Spider-Man in the 2012 film The Amazing Spider-Man and its 2014 sequel The Amazing Spider-Man 2.
 * Alfred Molina, who played Doctor Octopus in the 2004 Spider-Man sequel, was considered for the Eighth Doctor in the 1996 TV Movie.

whoisdoctorwho.co.uk
The website whoisdoctorwho.co.uk had a list of sightings of the Doctor from which people had ostensibly been submitting to Clive Finch, a conspiracy theorist character from TV: Rose.

A submission from Gustavo Lugo said that Gustavo saw the version of the Doctor shown on Clive's website — the Ninth Doctor — "a couple of weeks ago", trying to sell Spider-Man comics from the 1960s and 1970s. The store owner refused because "they looked too brand new to be original copies."