There is no easy answer to that.
Just figure out your minimum requirements (X MB of GPU memory) for game and assume you'll have those X MB available. And just ignore support for hardware if it has less than X MB memory.
There are some vendor specific extensions that could provide more detailed info about memory usage, but they are not always present in system:
NVX_gpu_memory_info
ATI_meminfo
(sorry I cannot post direct links, because forum forbids to have too many links in post)
For debugging OpenGL stuff you can use:
CodeXL from AMD:
http://developer.amd.com/tools-and-sdks/opencl-zone/codexl/ (this is former gDEBugger)
Nsight from Nvidia:
https://www.nvidia.com/object/nsight.html
Graphics Performance Analyzers from Intel:
https://software.intel.com/en-us/gpa
All tools are free and they work best when run on their own hardware (Nsight on Nvidia GPU, etc...). They might work when run on different hardware, but will provide less detailed information.
From open-source software apitrace is the best GL debugging tool:
https://apitrace.github.io/
There was also promising tool vogl from Valve, but it seems to be abandoned for almost a year already:
https://github.com/ValveSoftware/vogl
There's also very good Direct3D debugging tool RenderDoc from Crytek:
http://cryengine.com/renderdoc But currently it doesn't support OpenGL. They have said it might support GL in future.