Literally everywhere. Every digital link that is serial, be it just a UART, an SPI line, or PCIe, goes into some digital component that most likely would to think in words (like: bytes). That gives you the need for Serial-to-parallel and parallel-to-serial shift registers.
Things don't always work at exactly the same, constant speed. You need a FIFO buffer – that gives you the need for your SISO and PIPO registers. You can't have cheap RAM without these! In fact, I've never seen "parallel in, parallel out" shift registered being called that – usually, these are just called buffer or register.
A lot of the math underlying error correction, checksumming, (pseudo)random number generation or cryptography relies on evaluation of polynomials over finite fields – which are typically implemented in hard- or software as Linear-Feedback Shift Registers. So, that's your use case for serial-in, parallel-out, registers with a feedback.
The device you're reading this on has thousands of shift registers, in the silicon IC designs of the various digital parts it's made of – its CPU registers, the arithmetic units of the CPU, its memory controller, the memory itself, the USB, PCIe, display connections, the display panel itself, in its interface to the outside world, especially if that's wireless, quite likely in the logic that controls in which state the power supplies are in, in the thing that allows it to light up a single power LED, in its keyboard, in the way the audio chip DAC connects to the digital side, in the digital filter within that, …
In short: if you open a device, and it has a chip in it, unless that one chip is just an opamp or a NE555 or dumb voltage regulator, it contains at least one shift register, with very high probability.