Good description Mike and others in this thread. I think Wildlife in particular and unpredictable activities like bull fighting are clear examples. For me in my wildlife shooting with cameras other than a D4 what sometimes happens is I shoot my burst thinking I am getting peak of action, only to have something even more interesting happen next. But with a full buffer I miss these next shots. This happened to me on the weekend testing out my new D800E. I really appreciate this feature of my D4!
I can think of examples for pro sports shooters and remote cameras. Set up a remote for the 100 meter dash and let her rip for the entire race, able to catch any unexpected happenings. Of course that is 9 seconds but there are several seconds of high emotion photography right after the finish too.