Amount of VRAM in use?
Solution 1:
Note: As it stands it appears this is only valid for Nvidia cards, GPU-Z does not appear to be able to get this information on Ati cards.
You can see how much video memory is in use on any reasonably new Nvidia graphics card using GPU-z, which you can get from http://www.techpowerup.com/gpuz/
For example my card shows:
Note the "Memory Used" field. I believe this should be available on almost all current cards, though I don't have an Ati card to check.
Solution 2:
You can use HWiNFO to determine the percentage of video RAM in use. It shows up in the sensor readings as "GPU Memory Load" or "GPU Memory Utilization". HWiNFO does not work as confirmed by the original question's author.
For advanced users with NVIDIA cards, you can also try the official NVIDIA PerfKit software, which "gives you access to low-level performance counters inside the driver and hardware counters inside the GPU itself".
For advanced users with ATI cards, you can also try the official GPU PerfStudio software, which includes "a Frame Profiler that allows you to identify per draw call performance issues at the hardware counter level". This should give you access to the VRAM usage, but alas, I am an NVIDIA user, so I cannot test this for you.