I can't answer about MaC OS X, it's been too many years for me. Linux isn't an OS so there's no definitive answer there, but I can tell you about Debian-derived OSes (like Ubuntu), which are GNU-based OSes that can sometimes use the Linux kernel: try installing the libgl1-mesa-dev package. If you're asking about Android, another common OS that uses the Linux kernel, the GLES libraries should come with your devkit.

The answer to why your third-party software (skaslev-gl3w) uses GLX, well, you'd have to ask whoever developed it, but it's a handy and standard way to create a GL context on an X11 server.

On CentOS/RHEL, you're probably after the mesa-libGL-devel package.

http://rpm.pbone.net/index.php3/stat/4/idpl/17834939/dir/centos_5/com/mesa-libGL-devel-6.5.1-7.10.el5.i386.rpm.html

I simply need a pure OpenGL context 4.x, no extra lib, no fancy stuff, only the core… I’d really appreciate if anyone could help clear this up.

Problems is there's not really such as thing as a pure OpenGL context. You're going to need something to draw to.

Even if you're going full screen, you're not directly programming the GPU and you're not driving the video output chips, you need to go through the OS kernel. A typical modern OS kernel is design to prevent you from getting at the hardware directly: you need to ask it nicely at the very least if it will do you the favour of accessing the hardware on your behalf. On a GNU/Linux system, that means getting the X11 server to share nicely. On Mac OS X that means getting the Quartz service to share nicely. Even on Microsoft Windows you need to share nicely with other applications calling into the embedded display service. On Android you use EGL to share the flinger nicely.

There are cross-platform libraries that will get you an OpenGL context. That's what they're for and why they're there. SDL, for example, works very well on all the above platforms. If you insist on doing without such a library, the source is free so you can see how it works and reimplement it yourself. Of course, it might turn out SDL uses glx/wgl/egl underneath, because to do otherwise would reimplement all those ioctl/X11/port/SYS calls. Might be worth checking, though, or even just using the library directly.

The closest you can get to a "pure" OpenGL rendering context on X11 is by just using the X11 library itself.
Some of the older OpenGL books go into this but unfortunately it is becoming a bit of a lost art in the newer literature.

A good example is http://content.gpwiki.org/index.php/OpenGL:Tutorials:Setting_up_OpenGL_on_X11
As you can see, this uses GLX (which is what provides the rendering context).

Some more typical rendering contexts include...

glut
wxGLWidget (wxWidgets)
QtOpenGL (Qt)
Gtkglext (Gtk)
SDL

Personally, even though I am a C++ developer, I still highly recommend Glut. It is really portable and is already installed on most Linux distros. The 100% free implementation is called FreeGlut.

If you want something portable that gives you only the OpenGL context, and nothing more, then I recommend glfw. Well, it gives you a little more, like interface to I/O (e.g. mouse, keyboard). In my opinion, glfw is a stronger and cleaner library than glut.