When does the Kinetic Work Energy Theorem not apply to a situation? Or better, is there a general form of the equation where work can equal the change in any energy? What is work besides a force and a distance?
The Work-Energy Theorem only applies to rigid bodies. That is, if the work is not used to deform the object. There's a thread here that discusses this in detail; http://physics.stackexchange.com/questions/58134/how-to-understand-the-work-energy-theorem Work by definition, is what a force does on an object by displacing it. However, there are other ways of representing work if that's what you're asking.
Here's something that I wrote in another thread that may clarify how the "work"-energy theorem, when thought of as an application of Newton's 2nd law, may be applied to deformable bodies.
If the velocity doesn't change, the work-kinetic energy theorem just says that the net work must be zero. You do work when you lift an object at constant speed, but gravity is also doing negative work.