We present a novel distributed range-free technique called ExPLoIT for estimating geographical location of sensor nodes in mobile sensor networks. ExPLoIT is the first positioning technique that exploits location information at regular nodes in addition to using seeds. The key idea is the notion of confidence that a node has in its location estimate which can be used by other nodes for localization. Using Monte Carlo integration, a node estimates its current location and confidence based on its past location and the location information it receives from its neighbors. Node mobility is exploited to transitively localize the network. Our extensive simulation study shows that our proposal outperforms three other state-of-the-art range-free localization techniques under a wide range of conditions. The strength of ExPLoIT is that it is robust to irregular radio propagation, arbitrary seed and node density, and stochastic seed and node mobility; no special hardware is necessary at sensor nodes.