Do I need a hardware accelerator to run OpenGl applications?

I realize that for games in full screen, it would be necessary. But what about simple things like glxgears in smaller windows?

No, you don’t actually need an accelerator. But the only things that will run are very simple apps, like the blue/red book, Mesa demos, etc.

These should be ok in a window, but be warned even some of these may require an extension or two. If you look at the software OpenGL renderer for Win32, you won’t get the multitexture extension.