is there an API or profiler application that can track the video memory usage of my application?
I am using C++/OpenGL on Windows, but I am open to suggestions on other platforms as well.
On Mac OS X you have OpenGL Profiler.app, which comes with the Developer Tools (on the OS DVD or from http://developer.apple.com)
On Windows you could try gDEBugger - a good commercial OpenGL Profiling tool.