This paper proposes a decentralized state estimation scheme via network gossiping with applications in smart grid wide-area monitoring. The proposed scheme allows distributed control areas to solve for an accurate global state estimate collaboratively using the proposed Gossip-based Gauss-Newton (GGN) algorithm. Furthermore, the proposed scheme mitigates the influence of bad data by adaptively updating the noise variances and re-weighting the contributions of the most recent measurements for state estimation. Compared with other distributed techniques, our scheme via gossiping is more flexible and resilient in case of network reconfigurations and failures. We further prove that the power flow equations satisfy the sufficient condition for the GGN algorithm to converge to the desired solution. Simulations of the IEEE-118 system show that the proposed scheme estimates and tracks the global state robustly, and degrades gracefully when there are random failures and bad data.