I love watching the Special Features on DVDs because the "how" is almost more interesting to me than the "what." Some discs, like the 2005 King Kong, the 5-disc edition of Blade Runner, and the Bluray of Avatar really go all-out in detailing the process of movie-making. Knowing how much work went into each little detail only enhances my appreciation (for instance, for King Kong the crew extensively researched New York and basically re-created every building in downtown Manhattan as it would have appeared in 1933 for the biplane flyover scenes. Only a native New Yorker would notice.)
I also love watching blooper reels and deleted scenes. In most cases it is evident why scenes were deleted -- even though the running times of some other movies (Gone With The Wind, The Nymphomaniac) are sorely in need of trimming. Occasionally though I disagree with an editorial cut.
For instance, there was a whole sub-plot in Avatar about a love affair between Trudy the helicopter pilot and Norm the other Avatar driver. It humanized both characters and explained a couple plot points that otherwise were left hanging. In the 1933 King Kong a whole sequence called "The Spider Pit" was cut out because it was too graphic and slowed the pacing of the film. Peter Jackson put it back in for his 2005 remake (he also remade it in 1933 fashion for the re-release of the original) but I agree with the original omission. In Blade Runner Pris's death scene was considerably shortened, which was the right decision. The full-length version just goes on and on.