Concerning noncausal systems I suppose, it's unlikely that they exist and are used anywhere in real life. At least, I've never collided with such exotic cases. Imagine, the output signal of such system, according to its definition, should arise earlier, than the input one, provided the system had zero initial conditions. It's impossible, because it contradicts the law of energy preservation.
The second situation unstability is very actual. If the system possesse the reverse link (for example, transistor cascades) THEN IT MAY BE CAPABLE OF SELF-SIMULATION, which is caused by unstability. There are special criterions for continious-time and discrete-time signals, allowing to distinguish such systems.
With respect,
Dmitrij