bits manipulation (C)

I'm an autodidact and I have programmed in C for one year now, but never studied this topic. Apart from operating systems or embedded systems, when do we need to manipulate bits in 21st century ? If you could give some examples...

Off the top of my head:

* Reading and/or writing binary file formats (GIF, PNG, JPEG, MP3, ...)
* Hashing
* Cryptography
* Flags (in C and similar languages)
* Interacting with legacy code
* Anywhere overflow or roundoff errors are likely to be a problem:
** Bignum libraries
** 'Scientific' libraries
** Audio libraries
* Premature optimization