How can I tell which apps are using up my graphics memory? Sometimes my Macbook grinds to a halt due to the GPU's onboard memory getting full. (I know this because the CPU use, RAM use and disk use are all low, and because closing things like Chrome tabs and large pdfs tends to resolve the issue.) To avoid this, I'd like to be able to monitor the use of my system's graphics memory.

There doesn't seem to be an option in Activity Monitor, but is there some other way I can tell (a) how much graphics memory is currently free, and if possible (b) which apps are currently using the greatest amount of it?

I'd much prefer a free solution over a paid one; a Terminal-based solution would be fine.
I am not saying you are wrong, but the GPU memory is normally used for rendering the current laptop 2D display, and then for the calculations for 3D display (games), and GPU acceleration (modern browsers).  I've used, programmed various computers for many years, and yet to see an issue related to an application using to much GPU memory.  

But ISTRC MBP from 2010 onwards(?) have two GPU's the integrated (intel) and the discrete  (NVIDIA GeForce 320M in mine).  The MBP has good battery life due to when rendering text, images for the screen the low energy intel is used, but when game, videos are played and need more GPU processing is required the NVIDIA graphics chip is used.  Maybe you have an issue with the NVIDIA graphics?

It's maybe more likely that it could be a 'wait' caused by an issue with the filesystem, hard drive, or maybe elsewhere.  A failing hard drive will not report loads of activity when accessing a file that the hard drive controller takes extra long to read from. 

It may help people to help you if you say how often it happens, whether the spinning beach ball appears, if it's a case of just taking a few moments to close windows, and then it wakes up again quickly or slowly? 

Next time it happens try closing one application set of windows, say Chrome, and then wait (5 minutes) to see if that fixes it, and then the next try the other.  As it's likely to be only one application that is the main issue, and you'll do best in trying to narrow it down. 

I've MacBook that getting a little slow occasionally but it's not gotten to the point where I need to correct it.

Good Luck!