I first learned about bit-shifting when I took DIP / Computer Vision as an undergrad. All the assignments were done as plugins for ImageJ, which is apparently widely used in the scientific community (or so the course claimed). ImageJ stores the pixel values for images as bytes, ints, or longs (depending on the color-depth), so to get the individual component values from a 32-bit RGBA image (8 bits per channel), you would do something like this:

int pixel = image.get(x, y);

int alphaVal (pixel & 0xFF000000) >> 24;

int redVal = (pixel & 0x00FF0000) >> 16;

int greenVal = (pixel & 0x0000FF00) >> 8;

int blueVal = (pixel & 0x000000FF);

That's just one example w/ one piece of software, but I know similar approaches are often used within the world of imaging / graphics. Maybe networking? Seem like it would correlate well to IP address operations.