Assuming they weren't removed when the writers/directors changed the plot mid-shoot and therefore don't directly contradict anything left included in the film/tv show
It depends on the work in question and on whom you ask. They're at best lesser canon, but an answer based on a deleted scene would usually be acceptable.
At one end of the spectrum, we have Star Wars, which currently takes a very strict approach to canonicity, with the vast majority of its existing material falling under 'Legends' rather than canon. The accepted answer to Are deleted scenes considered canon? tells us that no, deleted scenes even from the seven main films count as Legends material.
At the far end of the spectrum, there's Doctor Who, which takes a much much (much) more lax approach to canonicity and is often said to "have no canon". There are TV shows, films, books, comics, and much more, all interacting and contradicting each other. Even within the TV show (the closest we can get to 'main canon'), there are frequent contradictions. The accepted answer to Is 'Time Crash' considered part of Doctor Who canon? says that even minisodes are "as close to canon as you get with Doctor Who", but deleted scenes are generally not considered "real".
But both of these are massive franchises with huge fanbases, and most films and TV shows haven't bothered specifying whether or not deleted scenes should be considered canon. At that point it depends on whom you ask. Personally I might consider deleted scenes to be canon unless they contradict something else in main canon. A quick search through questions on the main site threw up at least three questions from DVK in which he's looking for "canon including from interviews or deleted scenes", so seemingly he agrees with me on this one. Doubtless you'll also be able to find people who feel that deleted scenes are never canon.
In fact, even with the two franchises mentioned above, it's not as clear-cut as all that. Deleted scenes from Star Wars films often make it into the novelisations, which are considered canon when they elaborate on the films. For instance, Chewbacca ripping someone's arm off in TFA is canon even though this scene was deleted, and so is the existence of Constable Zuvio.
From the point of view of providing acceptable answers on this site, I would say that an answer based on a deleted scene is fine, provided you make clear that it is from a deleted scene (and preferably provide a link to that scene if possible). Sure, it might be a lesser level of canon than the non-deleted parts of the film, but the fact that we accept film-based answers to questions about Harry Potter, and novelisation-based answers to questions about Star Wars, shows that we're fine with answers based on lesser canon, provided it's clear that they are such.