Wireless sensor networks (WSNs) have attracted considerable attention in recent years and motivate a host of new challenges for distributed signal processing. The problem of distributed or decentralized estimation has often been considered in the context of parametric models. However, the success of parametric methods is limited by the appropriateness of the strong statistical assumptions made by the models. In this paper, a more flexible nonparametric model for distributed regression is considered that is applicable in a variety of WSN applications including field estimation. Here, starting with the standard regularized kernel least-squares estimator, a message-passing algorithm for distributed estimation in WSNs is derived. The algorithm can be viewed as an instantiation of the successive orthogonal projection (SOP) algorithm. Various practical aspects of the algorithm are discussed and several numerical simulations validate the potential of the approach.