I've seen some successful digitla photos that were well,well "into" a sequence of shots. One time my wife managed to take a simply wonderful shot of her sister's little child in his stroller in Hawaii...it was just a wonderful moment...it was shot #15 or #18 of a series, as I recall. She and I went through the series, and there were "almost" and "kill-file" shots, one after another, and then well,well into the shooting sequence was a simply outstanding shot of the boy relating to his older sister. We both agreed, that had she been shooting film, the shot never would have come into being, due to the cost of film.
The other point that arises is the way digital capture and in-field review can allow the photographer to select a shutter speed that is fast enough to capture rapidly-moving subject matter, and that at times "a little bit of blurring" will totally ruin a photo, and that digital capture makes it possible to get JUST the right effect, right there in the field. One commenter referred to this as "the Polaroid effect".
One thing I never really experienced was how sequential action (sports,mostly) could be captured with a professional-level camera with a pro-level autofocusing system; I learned on manual focus 35mm SLR's that topped out around 3.2 to 3.5 FPS; after getting a D2x with 5 to 8.2 FPS capability and powerful autofocus, it became possible to get action shots that were focused in situations where manual focus meant I would have needed to acquire, shoot, lose focus, re-acquire, shoot, lose, re-acquire focus...using an AF s-slr and a MF 35mm SLR of only 3.5 FPS is not the same thing.