But we do get to see deleted scenes from movies on DVDs, sometimes with commentary from the director about why they were deleted, and I think there are lessons to learn there (novels are not the same as movies, obviously, but they are both ways of telling stories).
First, different directors handle this differently. Woody Allen never saves what he removes from films; he tosses everything once he's done. Nowadays I'm sure directors save things (maybe even especially their darlings) just so they can appear on the DVD.
The most common reason I've heard directors cite for removing scenes is pacing. Especially toward the end of a movie, you don't want to lose momentum. If the scene reveals important information, is that information conveyed elsewhere (or can it be inserted somewhere else, or can we do without it)? If no vital information is being conveyed, save it for the DVD.
Pacing is important, but it's not the only consideration. Clint Eastwood's Midnight in the Garden of Good and Evil has a scene in the middle where John Kelso, the main character, goes to a very fancy cotillion which is disrupted by The Lady Chablis (who had been very disappointed that Kelso wouldn't take her as his date). This has nothing to do with the plot, and contains no vital information (the relationship between Kelso and Chablis is pretty thoroughly illustrated elsewhere), but it's funny as hell and Eastwood obviously decided to leave it in.
Pacing is important, as I say, but it isn't everything. Some artistic decisions can't be made by following the rule book.
Ben Affleck did an alternate ending scene for Gone Baby Gone, where a voiceover referred back to the film's opening to summarize the point of the film. Fortunately, he had the good judgment to remove it and let the audience think it through for themselves.
By the way, Robert Altman's most common reason for removing scenes was "too sentimental," which says a lot about his films. I will also mention that one of my favorite scenes in Gosford Park was not in the finished film. It was removed because it tied into a subplot that was removed, but it is a great scene and tells a lot about two of the characters. In my mental version of the film, it is there, where it belongs. 🙂
Sometimes scenes have to be removed because the plot shifts and they simply aren't possible. There was a really nice scene in A Sane Woman that I had to remove because it was a conversation that Jan and Marshall would never have had except in private, and at that point in the book the resolution was in motion and they would never have left the suspects alone even for a minute. I should locate that and post it here.
I have posted some deleted scenes here, and this is my favorite. It didn't fit in the book because the plot shifted, or it would be there. Oh, well.
(Of course, I'm sure some movie scenes are removed simply because they sucked, but those aren't likely to show up on DVDs. 🙂 )