Recent advances in metering technology, deregulation of the energy market, rapid penetration of renewables, and the smart grid vision for situational awareness, all call for a system-wide power system state estimation (PSSE). On the other hand, complexity of an interconnected power grid, privacy policies of local authorities, and vulnerability concerns preclude a centralized estimator. In this context, several possible manifestations of PSSE are treated in the present paper under a unified and systematic framework. Building on the alternating direction method of multipliers, a novel decentralized PSSE approach is developed. The obtained algorithm waives local observability concerns, leverages existing software, while requiring local system operators exchange minimal information only across tie lines. Numerical tests on two commonly used benchmarks, namely IEEE 14- and 118-bus power grids, show that the desired statistical accuracy is attained within 5-10 inter-area exchanges.