This is a somewhat naive question, which actually does not have a big answer for David's contribution. I'm not sure that any extension serves any useful purpose. So ask why you need to know?
After the standard C library, without a doubt, the main OS services for any OS that you use, after that you use any libraries that your application needs, therefore, although it may be right, ask "What are the most popular libraries for networks?" for example, your widely open question is impossible with anything that would either serve a useful purpose or confront a statistical study - it depends on who you ask and on what they work on.
Moreover, most higher-level libraries have lower-level dependencies, so when you think you use them, you actually use a lot. For example, matja offers libX11, but while most Linux and Unix GUIs use X11, you can never access X11 functions directly.