I would break the concept up into levels of "eating." Obviously the most complete version of eating is the one we are used to: between the mechanical crushing of our mouth and stomach, and the chemical reactions in the stomach and intestines, it turns the "food" into simple component molecules that can be transferred to anywhere in the body where they are needed.
For a different version, consider the human consumption of gold foil (why not?). We mechanically tear it into pieces which can travel through the digestive tract, but our chemical digestion does not occur with Gold. Instead it travels through relatively unharmed to be eliminated, with much of its physical layout intact.
The deciding factor between these is whether the creature actually gains from eating the material, or if it merely find its way into the digestive tract, to be eliminated later.
A third case would be to view "eating" as a defense mechanism. Instead of having a stinger or similar defense mechanism, if a creature could render its attacker inert by consuming it, it would be more than comfortable doing so, even if it did not gain any energy from it.
I think anything could be fair game along these lines, especially if you include defensive binge eating. A creature that can withstand massive massive heat could quickly disassemble and oxidize just about any compound (5000 degrees would be sufficient for everything shy of perhaps Tungsten). It would be an energy inefficient eating process, but it would work.
The only thing I think it could not eat would be a toxin crafted to take advantage of any digestive weakness it may have. For example, the creature would need to decide if something is food (using food processing mechanisms to acquire energy) or an enemy (using destructive mechanisms, which may cost energy). An enemy which appears to be food could subsist long enough to do internal damage. Such a toxin would have to be highly specialized.
One interesting direction to take is that "interesting" things would happened to try to eat exotic things. For example, if there was a way to turn a creature inside out without killing it, what would happen if one creature ate its inside out breatheren? (This is similar to the argument in DnD about turning a bag of holding inside out). A specialized toxin might try to emulate the sensation of eating its bretheren in hopes of preventing a destructive digestion from occurring.