The very short answer is that canon within the Matrix-'verse is pretty complicated and certainly we should start out by pointing out that no-one within the production team has ever clearly defined what represents the official canon status of the film's subsidiary properties. On top of that, there's the additional wrinkle that some of the webcomics are clearly intended to be parodical, some were removed from the website (and not subsequently republished) and some of them seem to directly conflict with the movies.
The Animatrix and Matrix video games are slightly easier to categorise, but even so there are individual stories that link to the movies and other stories that are set entirely apart from the movies.
What elements make up the main 'canon' of the world of the Matrix (and why)?
Obligatory xkcd reference
- Final Flight of the Osiris. This story (written by the Wachowskis) sits directly between the first two films and establishes how Zion learned that the machines were intending to attack from the surface.
- The Second Renaissance, Parts I and II. This story (based directly on the Wachowskis 'Bits and Pieces of Information') serves as a direct prequel to the Matrix Trilogy and explains how the Machine War began.
- Kid's Story - This story establishes the character of "The Kid" and explains his presence in the second and third movie.
Webcomics & Comic Anthologies.
Bits and Pieces of Information - Written by the Wachowskis and featured in Matrix Comics: Volume 1, this story provides extensive back-story into the events leading up to the Machine War, specifically the birth of AI and the first Machine Rebellion.
Saviors - Commissioned for the Matrix Comic: Volume 2, this story references the problems of removing older inhabitants from the Matrix as well as showing a character who's been "re-inserted" and given a new identity as a reward for his decision to cooperate with the machines.
The two AAA-rated Matrix video games contain cut-scenes and additional information that bear directly on the plot of the subsequent films. They were designed under direct consultation with the Wachowskis.
Enter the Matrix - Filmed alongside the movie sequels, the cut-scenes tell the 'parallel story' of Niobe/Ghost and the crew of the Logos as they seek to support Neo and the crew of the Nebuchadnezzar. Additional information is provided on the Oracle and Seraph's relationship as well as the conduct of the War.
The Matrix: Path of Neo - Released two years after Enter the Matrix, Path of Neo details Neo's training as well as allowing you follow the "cinematic path" of the movies. No major new information is imparted, but the scenes were hand-picked by the Wachowskis and the game features a cut-scene that offers a rare 'directors commentary' about the ending of the film trilogy.
What elements are arguably canon?
The other stories from the Animatrix; Program, World Record, Beyond, A Detective Story and Matriculated are all stand-alone pieces. With the exception of a nice voice cameo from Carrie-Anne Moss in 'A Detective Story', none of these were produced in conjunction with the original cast/crew. Importantly, none of them conflict with what we know about the world of the Matrix, as seen in the film series.
Described as the "official continuation" of the Matrix universe, this game at least had the blessing of the Wachowskis. The plot veers off in such wild directions that's it's essentially impossible to categorise it as a truly canon extension of the film series:
Those are the people, the people who thought about it, who worked at
it, who we ultimately made the trilogy for and it now makes perfect
sense to us that they should inherit the storyline. - Larry Wachowski
Aside from Get it? and Who says you can't get good help these days?, all of the the other webcomic stories (including Day In.. Day Out) seem to be internally consistent with the rules and plots laid out in the films. The sole exception is Goliath which takes a dramatically different tack than the films, featuring an alien apocalypse.
A collection of stories set in the world of the Matrix. The stories
stand alone. They are not adaptations. - Matrix Comics - Series One - Preface
What elements are definitely non-canon?
As mentioned, Get it? and Who says you can't get good help these days? were always intended as parodies and are clearly not intended to be canon to the Matrix universe.
There were various web-based games available on the Matrix website such as Tunnel Recon, Pill Game and Dock Defense that were clearly intended to be tie-ins rather than canonically accurate.