Two-state systems are the simplest non-trivial quantum systems that occur in nature however it should be noted that the above mentioned methods of analysis are not just valid for simple two-state systems.
Another case where the effective two-state formalism is valid is when the system under consideration has two levels that are effectively decoupled from the system, this is the case in the analysis of the spontaneous or stimulated emission of light by atoms and that of Charge qubits.