What is "Canon"?
Star Trek canon is defined as:
the television / streaming series
Star Trek (The Original Series) (TOS),
Star Trek: The Animated Series (TAS),
Star Trek: The Next Generation (TNG),
Star Trek: Deep Space Nine (DS9),
Star Trek: Voyager (VOY),
Star Trek: Enterprise (ENT),
Star Trek: Discovery (DIS),
Star Trek Short Treks (ST),
Star Trek: Picard (PIC),
Star Trek: Lower Decks (LD),
Star Trek: Prodigy (PRO), and
Star Trek: Strange New Worlds (SNW);
the film series
The Motion Picture (ST I or TMP),
The Wrath of Khan (ST II or TWK),
The Search For Spock (ST III or TSS),
The Voyage Home (ST IV or TVH),
The Final Frontier (ST V or TFF),
The Undiscovered Country (ST VI or TUC),
Generations (ST VII or GEN),
First Contact (ST VIII or FC),
Insurrection (ST IX or INS), and
Nemesis (ST X or NEM);
and the reboot film series
Star Trek (2009) (ST 09),
Into Darkness (ST ID), and
Beyond (ST BEY).
Alpha Canon includes officially licensed print materials, such as movie tie-in comics, novelizations of canon productions, and the like.
Beta Canon includes productions licensed by CBS or Paramount Pictures but not produced by either, such as novels and other published works of fiction and non-fiction.
For the sake of this guide, only official canon material is acknowledged.
Editor's Notes: When canon is found to contradict itself, we find it best to assume the newest information to be official as long as it can be justified in universe. Otherwise, assume it is correct for that series / movie.
While not canon, "Star Trek Continues" has been included in our lists. The fan-made series is true to the spirit of Roddenberry's vision and delivers quality writing, acting, and film editing.
Is the Millennium Falcon in the Star Trek canonical universe?
Yes. In "Star Trek: First Contact", Starfleet received some assistance from the ship that could make the Kessel Run in fourteen twelve parsecs.
Reference: This article at Eggpedia
The Official Star Trek Cannon fires Star Trek DVDs and is wholly ineffective as a siege weapon.