I'll answer this with sincerity. OpenGL is, well, open. DirectX...not so much. DirectX is proprietary and is used by Microsoft OS's only. I have not looked at all the code concerning OpenGL so I can not say for certain, but what I have seen was mostly C++ with a dash of C thrown in.
DirectX is bits of C, C++, x86 assembler, as well as a proprietary scripting laguage used within Microsoft.
It IS possible to use DirectX in *nix but the work involved is more than it's work, IMHO. A couple of friends and I did it ONCE with DirectX 7 and after patting ourselves on the back, swore we wouldn't do it again.
So to answer your post, for most things 3D in Linux, OpenGL is probably your best bet.

Can opengl games run on windows?
In the market, i can see that most games like Warcraft/Half life/Doom 3 will require you to update your Directx.
I had seen books about opengl in windows, seems that windows can run opengl plus directx.
In current linux like Suse, what is its graphix format? Opengl?

There's a native Linux version of Doom3 which plays flawlessly...

DirectX isn't just a graphics API, you should be comparing Direct3D and OpenGL. Yes TigerLinux, Windows can run OpenGL..

Excellent clarification, cs-cam.

Windows OS's can use OpenGL. The majority of games for Windows utilize DirectX because it is more convenient to use a single package that can handle graphics and high definition sound.
The only company I can think of off-hand that regularly uses OpenGL in their games is LucasArts.

However, I should note that just because a game uses OpenGL in Windows or Linux, that does not mean it can be easily ported to the other OS. There are many OS specific processes happening in the background, particularly with starting or exiting a game.