I think the point is that your question in general is overly broad. What are you trying to code? A console app will be very different from a win app. A game will be very different from a business type app.

For example, if you just want to code a game that will run in nix, then pick an appropriate set of libraries that will do the trick.

This is one I have toyed with. You can compile for win or nix. You call irr api functions to create windows and render fx, so it adds a layer of code, but in doing so it makes you platform independant.

http://irrlicht.sourceforge.net/features.html

Any number of libs/API's are good. Let us know what you are trying to build and you will get much more helpful suggestions.

The closest you will get to Windows API in Linux is 'The X Window system API'
If you have X11 (xorg) installed in linux, which most desktop users have, this API will be available. Unlike windows it is possible to install Linux without any window system, if thats the case this API is not available.

It has many of the same characteristics as Windows API, like good availability and hard to use due to being an old and low level API.

Basic tutorial
The X Window system