EDIT: Long post ahead. You've been warned.
Regarding canonicity (is that word?

) both in the manga and anime: we're ignoring retcons and plotholes. It's the creation of plotholes that creates the difference in opinion regarding what is and isn't canon, since most retcons relating to both the manga and anime are "because I said so." Those kinds of retcons never go over well with fans, which is why we tend to ignore the retcons and decide for ourselves what is and isn't canon.
For instance, #19 and #20 show up first for no reason, #17 and #18 are stronger in Timeline 1 than in TL2, and #16 is present. Retcon: It's later eplained that Trunks' appearence in other timelines might cause there to be changes and that not all timelines are necessarily the same to begin with. That's the kind of retcon fans can easily accept. Meanwhile, plotholes like Movie 1 and the Raditz saga being ignored as a retcon will be cause for strife. The same goes with unnecessary retcons like the Kanzenban had. Though fans enjoyed seeing something new, it causes another rift.
Olivier Hague wrote:I keep hearing things about the Daizenshû claiming that a couple of movies did "happen" (could someone provide the original quote? I'm intrigued)...
Entries in the chronology of Daizenshuu 7 make reference to movies 1 and 5:
"
761: Goku battles the forces of Garlic Jr, the kidnapper of his son Gohan." (The next entry is for October 12, 761 and talks about the Raditz saga.)
Under 763:
"
One day in October: The planet Makyo approaches the Earth as it did 5000 years ago. Garlic Jr unleashes his revenge upon Gohan and his friends. (Obviously this is the Garlic Jr saga and not a movie)
First 2 entries for 764:
"
One day in August: Goku's return to Earth. Trunks also arrives on Earth and defeats Freeza and his father."
"
764-767: Cooler attacks the Earth. Goku confronts him."
The next entry for 764 talks about Vegeta training in a gravity room, Bulma falling in love with him, and Goku and Piccolo going to driving school. The next entry is for 766, stating that Trunks is born, and the next entry is about 767. It's first entry states that it is the year Goten is born in, then skips to numerous entries for May; May 7 being when Satan and Videl won the 24th budokai, and then May 12th-26th being the arrival of the Androids to the death of Goku. May 27 lists Goku's funeral and Trunks returning to the future. The last entry in 767 is about the Otherworld Tournament, taking place "one day between May and June." After that, it jumps to an entry for 770 in which Krillin and #18 get married. In other words, no entry for #9 being canon is made.
As for the movie 7 semi-canonicity claims that I and others make, note that the plothole regarding how the Trunks from Timeline 3 (the future timeline in which Cell originated from) was able to destroy the anroids of TL3 was solved by the daizenshuu. It explained that there are 4 timelines:
Timeline 1: The story we see, the anime and manga's timeline.
Timeline 2: The timeline that Future Trunks comes from.
Timeline 3: The timeline that Cell comes from. In 784 Trunks, like the Trunks from TL2, goes into the past. This Trunks goes into Timeline 4, where he obtains the remote detonator, which he uses to destroy androids of his timeline.
Timeline 4: The timeline that TL3 Trunks traveled to. For it's mini-chronology, it shows that it's identical to TL1 up to 767, where it shows that instead saying "Androids Appear. Cell Games debut," it just mentions the Cell Games. In the goes on to explain that the outcome of its Cell Games are unknown since Trunks was never present, as Trunks went back to his timeline and got killed.
That last bit creates a plothole, however, since Cell never arrived from any alternate timeline. Not only that, but how did he achieve perfect form if #17 and #18 were destroyed. This is why I and others say it should have been movie 7 instead. To explain the plotholes of movie 7, we can simply say that the Timeline differences could explain how the androids were defeated when they first appeared, as well as mention that Gero's computer perfected #13, #14, #15 instead of perfecting Cell. If a future Cell made no appearence in TL4, then Trunks and Krillin would have no reason to blow up Gero's sub-lab.
EDIT: Also, the bio for Trunks mentions that "We also learn from the anime that the sword used by Mirai Trunks was given to him by Tapion." There are no mentions regarding whether or not movie 13 is canon or how a Mirai Tapion could have existed.