Canon is not strictly defined in the Matrix franchise. The three films, The Matrix, The Matrix Reloaded and The Matrix Revolutions form the main core of the series, with additional short animated films (The Animatrix), video games (Enter the Matrix, The Matrix: Path of Neo, and The Matrix Online) and comics (The Matrix Comics) created by the Wachowskis and other artists. Some of these tie directly into the films, while others are more ambiguous.
The Animatrix and The Matrix Comics
The Wachowskis wrote works in other media which tie directly into the story of the films, such as Final Flight of the Osiris and Kid's Story, as well as backstory to the universe, in Bits and Pieces of Information (which was retold and expanded by Mahiro Maeda in The Second Renaissance).
They commissioned other segments of The Animatrix, and The Matrix Comics to allow other artists' interpretations of the universe, which vary in how closely they follow the Wachowskis' vision. Some of these, like Get It? and Who Says You Can't Get Good Help These Days? are written as parodies rather than to be taken seriously.
Enter the Matrix
The Wachowskis also wrote Enter the Matrix, which takes place before and during the events of The Matrix Reloaded, and allows the player to follow either Niobe or Ghost. The plot diverges depending on which character you choose, raising questions over which of the two storylines is definitive.
Path of Neo
The Matrix: Path of Neo follows the plot of the three films, with some extra parts set between them, but also adds in some scenes that are only there to benefit gameplay, and training dialog that breaks the fourth wall (e.g. referring to which buttons to press). The "final boss" ending of the game is very different to that of The Matrix Revolutions, which the Wachowskis explain in a short speech before the action takes place.
The Matrix Online
The Matrix Online continues the story after the end of The Matrix Revolutions, with the first chapters written by Paul Chadwick, and continued by the game staff, but with the intention of allowing the players to shape the future of the Matrix. The game contained a number of servers (nine at first, later merged to three), which followed the same plot, but each of which had various unique events. Before the game was shut down all players were given every in-game power before being killed; this can also safely be assumed not to be considered as a continuation of the story.