Earlier quoted context omitted.
Endian is probably the most common.
Endian-ness would be reversing bytes, not bits within bytes, like 0x1234 -> 0x3412. What we're talking about here would be more along the lines of: 0b0010001 -> 0b1000100 The most obvious application I can think of for reversing bits within a byte would be for image processing applications, such as mirroring an image horizontally, or making kaleidoscopes. There are probably signal processing applications, too...
...but only a 2-color image.