One of the most fascinating design insights that I've come across recently is from Martin Lindstrom, author of Buy•ology.
In 1915 the designer of Coca-Cola's bottle was given a simple yet brilliant brief: design the bottle systematically and so distinctive that, if smashed, a single piece of glass would be recognizable as, and signify the Coke brand. Lindstrom describes this approach as designing "smashable components".
(This is a rather large fragment but you get the point. The ridges and overall shape make even a small piece very recognizable.)
Tiffany's signature blue box dates back to 1837 and is an excellent example of a brand that stands up to the smashability test. All you need to see is a hint of the telltale hue. Even at a considerable distance that Tiffany color is unmistakable. An interesting fact: On average, a woman's heart rate will increase by 22 percent when she is exposed to this color.
Distinctiveness gets talked about a lot in design and marketing but rarely gets implemented with any bravery. Most brands play follow the leader. Remember about 10 years ago when a slew of financial services firms redesigned their identity's in red. Red, given its negative connotations in finance ("in the red") had long been a big taboo, but when a leader in a category makes a bold move, the rest stupidly follow. Even Chase got on the red wagon following the merger with JP Morgan.
I remember first seeing GE trucks with the logos running off the vehicle's edges in the early 90s. Cropping into a logo, in any way whatsoever, has always been a serious violation of identity design principles. However, it does make for a much more dynamic look and breathes a little life into a recognizable logo that has been around for a very long time.
There is one another important thing to consider in partial displays, like the GE logo above, and recognizable fragments of a brand's design, they give the viewer's mind a more active role in the perceptual process. Instead of just recognizing an image or object, the viewer must fill in the missing details to compete the perceptual process of creating "meaning".