Do most OpenGL 2.0 and 2.1 graphics cards that still are in use support frame buffer objects (through the GL_ARB_framebuffer_object or GL_EXT_framebuffer_object extensions)?
In my experience, they do.
Among nVidia, GPUs at least as far back as the GeForce FX 5xxx (which support OpenGL 2.0) have FBO support, and I suspect even older cards do.
Among ATI GPUs old enough to only support OpenGL 2.0, I have seen such GPUs as the HD 2400 and the X1300, and they all support FBOs.
Among Intel GPUs, I think that it is mainly the HD Graphics families that have OpenGL 2.0 support at all, and all the HD Graphics GPUs I've seen have FBO support. I have also seen some other GPUs with 2.0 and FBO support, including some versions of the 965, and something called the "Eaglelake". I'm not sure why only some 965s support OpenGL 2.0, though. It could be a driver issue.
I have, on the other hand, not yet found any 2.0-compatible GPUs that do not support FBOs.
I hope this purely empirical answer helps somewhat.