Canon

Canon would refer to the body of works related to a particular subject and considered proper history and continuity to series. The Doom series may contain more than one canon based on storylines of various reboot universes.

See also Timeline.

Background
In case of Doom there are very few official comments that relate to canon or discuss canon directly. Sometimes official positions are contradictory or changes over time (or retcone are made).

As such there are a number of fan theories as to what comprises canon or what is not canon these can only be considered Fanon as their is very little as far as confirmation on what is canon.

In addition the Doom series has received a number of spinoffs and reboots throughout its life as well as tie ins.

Each reboot could be considered separate canons or alternate universes as part of a multiverse (Quake Arena backstory for example, Arena Eternal outside time and space, with heroes from various “alternate universes”).

Tom Hall and John Romero have confirmed that several ID series are in fact connected. Doom Marine is a Blazkowicz descended from Commander Keen, and William J. Blazkowicz before him (this does not apply to the MachineGames reboot universe however which follows its own universe with an alternate history for B.J. And different family tree). This is also mentioned in Doom RPG series as well. See ID multiverse timeline.

In both Doom RPG and Doom 3 boxset the hero for most of the games is alluded to be the same hero in Doom 1-3 (and the RPG series).

Quake Champions brings back Doom (Quake III Arena), now listed as Doom Slayer, and mentions his pet Daisy confirming a link between Doom 2016 and Doom 1. Doom Slayer also comes with his uniforms from Doom 2016 (Praetor Suit), Doom Classic (Doomguy), Quake Arena (Arena), and Doom 3 (Doom Marine), and biography details that links all the games together.

The game also brings new MachineGames William Blazkowicz from his “universe” to the Arena Eternal (the place outside of time and space).

The Fanon tends to argue against the veracity of some of these sources, assigning different levels of theorized canonicity to the various references. But for most part ID’s internal position is not known.

Crossovers

 * Wolfenstein, Commander Keen, and Doom are connected according to Tom Hall.
 * Wolfenstein RPG and Doom RPGs include crossover material with a number of ID series and each other.
 * Doom II RPG and Doom Resurrection have references to each other.
 * There are some crossover material between Doom, Doom 3, Doom (2016) and Quake Arena III, Quake Champions. The latter also has crossover with MachineGames Wolfenstein universe.
 * There are crossover elements in R.A.G.E. such as Mixom corporation. However the game is likely in a parallel universe where earth asteroid hit earth on August 23, 2029, and main character wakes up 108 years later in 2135 which is only a few years before Doom 3/4 which are each set roughly in 2145-2149. Based on what is known about earth in Doom series its unlikely its as bad off as it was in Rage 10-20 years before.
 * Doom 2016 and Doom 3 are likely in alternate earth universes, although the same Marine apparently travelled through time and space to both according to Quake Champions, and info in Doom 2016.
 * A comic in Quake for Saturn included and adventure following Quake Marines Dank and Scud run into the Doom Marine during their adventures. Assuming that Quake took place between 2008 and 2108, he'd either have had to have time travelled, interdimensional traveled, or the date would have to be set closer to the original Doom Timeline in the early 2020s.
 * Although Doom 3 is said to be in same universe as Doom I and II (and Doom RPG) it is unknown if it is a prequel or a sequel in some fashion. Quake Champions is not clear, but just includes elements of the story in the back information for Doom Slayer. The backstory for the Marine/Slayer is similar to manual prologue in Doom 1, however assuming that Doom took place in early 21st century (as per SNES and novels), then Doom 3 would have to occur in the far future (almost 120 years later) which would have problems with Doom 64 (unless Doom 64 was after Doom 3 and Doom RPG), but this would require for Doom Marine to have gone into stasis at some point on Earth most likely, before returning Mars. Doom 64 is implied in Doom 2016 and even more strongly in Quake Champions to be events that lead up to 2016 game.
 * Keel in Quake Champions appears to be based on Revenants.