That's kind of a broad question. Strictly speaking, no, if it's not in the final aired/premiered version of the show/film, it didn't happen. Realistically though, I'd say it depends on the content of the particular scene. As long as whatever it is doesn't conflict with established canon, then it's fine. Is there a particular scene you're thinking of?
Nothing particular. Someone on the Star Trek XI forum expressed a thought on the possibility of an extended BR version of ST when it's released on DVD and that got me wondering if they are canon or not so I posted the question.
I would tend to agree but if you are going to engage in debate on these boards then you have to refer to it.
If the reason you're asking is an extended version of a film that reintegrates deleted scenes, then of course the answer is : Yes, deleted scenes are canon. They're in the (extended) movie, aren't they? That said, the rule of "canon" (sorry, the term has been so overused and misused and abused, I cannot take it that seriously anymore) says that anything seen on screen qualifies. Deleted scenes were filmed, they can be seen, just usually outside of the actual film. Most of them don't really add any information that would be worth discussion. I mean, do we really care if (per STV's deleted scenes), Mt. Rushmore has a fifth President added to the rockface? Probably no. I guess you can just decide for yourself if you want to picture 23rd century Mt. rushmore that way or not. As for Saavik's ethnicity, it might be more interesting. Saying she's half Romulan explains a lot about her character in STII, but then again, the line was cut, and STIII operates on the clear assumption that she's a full Vulcan. So that should be considered "canon".
Hmm I am not sure if they are canon or not. One pretty big deleted scene I can think of is Dr.Crusher leaving the Enterprise to join Starfleet Medical in a deleted scene in Nemesis. In the deleted scene she leaves the Enterprise for her new job and there is a pretty touching moment where she says she will save the last dance for Picard (at a party they are having on Earth). But since that scene was not in the movie its hard to say "canon-wise" if she is still on the Enterprise or not.
Don't remember Nemesis that well (who does? ) but was there anything in dialogue at the end of the film that said she was leaving?
There was no dialogue anywhere in the film that suggested she was leaving. I believe her departure was supposed to be first mentioned as part of Picard's wedding toast. I'd look it up to be sure, but I don't feel like making my eyes bleed today.
The missing scenes in The Wrath of Khan were added back in for the special edition DVD release which helped the story some (although everybody knew Preston was Scotty's nephew). One thing the novelixation did mention IIRC is that during an emergency Bridge commands override all turbolift controls, even when transporting a wounded crewmwmber. When Kirk went to leave the bridge and th edoors opened, SCotty was there not because he wanted to show Kirk th ebody, but because the request for a lift overrode the nearest turbolift car. Off topic but interesting.
Deleted Scenes and home video Director's cuts This is a great thread. I believe that as fans of a film more is always better. Deleted scenes, storyboards for never shot sequences, screentests, extended scenes. Now when you are speaking of Star Trek canon I would say that when a film is released to the cinema whatever is on the screen is canon. When it gets released on home video as a 'Director's cut', 'Special Edition' or whatever you want to call it with deleted scenes added back into the film then that content officially becomes canon. The period of time between the cinema release and the home video release with these scenes could be 25 years as ST:TMP was, or could be 6 months or 1 year as probably will be the case with ST:XI.
According to Memory Beta, Madden showed up in the Nemesis novelization exactly like in the Nemesis movie deleted scenes, but was not mentioned again in the relaunch novels. Exception being in 'Q&A' where in an alternate universe he is XO of the Enterprise-E.
Nope the only mention was in the deleted scenes. No dialogue about Dr.Crusher leaving the Enterprise actually made it into the final film other than the deleted scenes.