Supposedly, the most popular "special feature" on DVDs is the Deleted Scene section, which is kind of funny if you think about it. In screenwriting, every scene is supposed to drive the story forward, or have some significance to the main plot. If a scene can be easily removed without affecting anything, then the conventional wisdom is that it's a weak scene.
Or to put it another way, these scenes weren't good enough to make the cut the first time, so why is anyone interested in seeing the leftovers?
Admittedly, there are deleted scenes that are fascinating to watch, at least in terms of seeing why certain decisions were made. Sometimes scenes get cut only to keep the pace moving, or to bring down the running time. In other cases there might be external factors, such as test audiences saying they hated the original ending. However, if you listen to commentary on many of these sorts of scenes, a common theme often emerges - "We just didn't need this scene to tell the story."
This is why when I'm in the rewrite stage of my script - and especially when I need to bring the page count down - I scrutinize every scene. I take each scene on its own and ask myself what it's doing for the story. Is it advancing the plot? Are we learning new information? Does it reveal something interesting about the characters? The big question I ask myself is - do I think this moment is destined to be seen only in the bonus features section of the inevitable DVD release? For whatever reason, thinking of editing in those terms helps me the most.
(Sidebar: today's DVD consumers probably don't appreciate the access they have to those mythic scenes. I remember the days when viewers only learned about cut scenes from the occasional still photo, or from reading the novelization. If you were lucky, the network TV showings of a film would incorporate some of the cut scenes to pad out the running time. It took nearly 30 years for audiences to see the Brando scenes cut from Superman II, and about 10 years to see the original ending to Star Trek: Generations. That was enough time for them to take on a near mythic quality among hard-core fans.)