Just to clarify to MrJoshL, we don't really "choose" what implementation to use (unless we want to force software rendering and we explicitly do so)
If we want hardware acceleration (aka get access to GPU), we'll just load the OpenGL implementation that is installed in the system (for NVIDIA cards, it's NVIDIA's, for ATI cards, it's ATI's). Since they're implementations, they implement everything they're supposed to, otherwise we would get a crash or a "cannot load routine from library" error and exit.
In Windows, the OGL system is called OpenGL "ICD" (Installable Client Driver). When the driver (ati, nvidia, intel, sis, s3, powervr, 3dfx, etc) didn't provide an OpenGL implementation, the application will be routed to a software implementation developed by Microsoft which is very outdated (supports 1.1 spec) so if you're using something higher, your application it will just fail to load (it's as if DirectX wouldn't be installed for Direct3D games)
When the driver did provide the implementation, the ICD will route to the driver's DLL.
In Linux, something very similar happens. Most distros ship the Mesa software implementation (which is usually very up to date), and if you install proprietary drivers, the installation messes with distro's folders & symbolic links to use the driver's OGL implementation instead of Mesa's.
Every now and then the installer (either driver's or distro's package manager) may mess the installation and try to mix Mesa dlls with driver's and X11 will crash when launching a GL application (been there....... multiple times). The situation has improved a lot though, in the last couple of years.
In Mac, I have no idea how it works, but afaik Apple controls the implementation being shipped.
You can of course ship your game with Mesa DLLs (since it's the only implementation I'm aware of that could be licensed for that) and always use Mesa's implementation, but almost nobody would like to do that.
GLUT & FreeGLUT are layers that simplify the creation of a GL context, and may deal with all this trouble (i.e. not having the right ICD installed, not having required GL version, loading extensions, etc) because this is all messing with DLL & function loading that has nothing to do with rendering triangles to the screen.
Edit: We just want to load the installed implementation and start rendering with hardware acceleration.