John Carmack (Quake series, Doom series, and the upcoming Rage engine) chose to use openGL rather than Direct-X -- that's saying something. Also, Call Of Duty series and Far Cry are notable games/series using openGL.
OpenGL appeals to me (as an end-user only, I know nothing about programming) because it's free, non-proprietary, and is managed by the Khronos Group who also manages openCL. And openCL seems much more significant, at this point, than openGL -- using the graphics card to significantly speed up general computation. At this point it's CUDA (which is arguably better, at the moment) or openCL -- free and works on everything or proprietary and only works on Nvidia hardware.
I realize this is a convoluted and indirect reason to like openGL, but I want the software to succeed that's not owned by a private company that gets to dictate what hardware we have to buy and who can use the software.
Besides, have you seen smallluxgpu (openGL rendering program)? Tell me that's not awesome.