LOTR's extended editions are all great, but I have to single out a two minute scene added for The Two Towers. It's a family reunion of sorts between Boromir (Sean Bean), his brother Faramir (David Wyndham) and their father Denethor (John Noble), told in flashback during happier times.

It ties together all the actions of Boromir in the first movie (why he knows so much about the ring already, and why he scheming to get it,) Faramir's incredibly heroic actions in the second movie (he lets Frodo and the ring go, knowing that keeping them will mean finally winning his father's respect) and Denethor's madness in the third movie (we realize he knows he is responsible for sending his most beloved son to his death.)

I realize that the theatrical cut of Towers weighed in at over three hours anyway, and director Peter Jackson was under serious pressure from the studio to cut anything not critically, 100% necessary. But I just wish they could have somehow saved this scene. It adds another layer of emotional complexity to the whole trilogy.