Remember that when talking about DirectX vs OpenGL your not talking about equivelent technologies.
DirectX is all around thing for building applications and games from. It handles not only 3d graphics, but sound, probably some window/menu stuff (not sure), and mouse keyboard stuff.
OpenGL is purely 3d graphics only.
There are other aspects that seperate them.
OpenGL is a industry standard. It's specifications are set by a wide veriaty of companies and industry groups. Its standards are slower to adapt new technologies then Direct3d/DirectX, but it's extensable. There are groups of extensions that are almost standards that incorporate most of what new stuff that Direct3d can do. Stuff like the pixel shaders and stuff (which is nessicary, I suppose, for building GUI's using OpenGL).
OpenGL is very cross-platform. This makes it suitable for building things other then games. 3d modelling applications, imagining software, CAD, that sort of thing. DirectX may be very good for games, but that's about it.
The closest thing to DirectX that you can find for Linux/Unix/OS X/Windows is LibSDL.
LibSDL adds a extra thin layer of abstraction over OpenGL, and takes care of things like weither or not you have 3d acceleration aviable and such. So if you write a application using SDL it can dynamicly take care of it so that you don't have to.
It also has the ability to take care of sound, menu/GUI stuff for games and applications, and take care of mouse/joystick/keyboard stuff. That sort of thing. Then you have stuff like higher level languages that can use LibSDL like python with pygame modules. There are a few games that do custom OpenGL work for the 3d engine, SDL for everything else, and then python for scripting character roles and stuff that isn't speed critical.
The Unreal Tournament 2003/2004 port to Linux uses LibSDL for most of it's stuff. It uses OpenAL for sound, though. There is some eye candy that you loose, but it's nothing important to gameplay and it's not noticable unless you know it's missing. Stuff like on the warthog car thing you don't get to read what it says on the license plate. LibSDL isn't a full featured as DirectX, but it's perfectly usefull for most things.
For a long time lots of Windows games used OpenGL for the actual engine, but uses DirectX anyways. So many "directx' games actually used OpenGL for a large part of what they did. Black & White is one game that I know for a fact does this and even Quake3 required a certain level of DirectX for you to run it. Lots of times they use it for menus or splash screens and such. I don't think it's as common as it used to be though.
Also you can use
LibSDL for making things like media players and such.
It's not as nice as DirectX, it's not as full-featured. But there are practical advantages to it such as it's cross-platform aspect and it's openness and there is no associated issues with licensing costs or any such thing. Plus for the customers it opens up things for enthusiasts a bit. Like I've heard that it's possible to get signifiant improvements in performance of the Linux version of UT2004 if you change out the default libSDL libraries that get installed along with the binaries of it with newer versions or custom-compiled and optimized versions.
If you want to make simple games that aren't speed critical using stuff like pygame with Python can make it VERY easy compared to programming OpenGL or DirectX stuff (plus you can compile python programs into binaries so that Windows users don't have to deal with all the dependancy issues). Hell they even have language bindings for PHP if your a web developer.
Also remember that games like Ut2004 and Doom3 are using Ogg Vorbis sound for games and such (Ogg Vorbis has always had the ability to handle up to 255 different channels for sound) and many indie games heavily use LibSDL and similar free libraries so Free sofware is slowly making it's way into gaming, too.
edit:
Also people are starting to get into building free software 3d engines for gaming. There is
Orge for instance. Another one is
crystal space. Also there are few hacked up versions of Quake1/Quake2 that are suitable for making your own games from. If your curious even Half Life2 still have remnants of original Quake 1 code in it.