We propose Cloud of Things for sensing-as-a-service: a global architecture that scales up cloud computing by exploiting the global sensing resources of the Internet of Things (IoT) to enable remote sensing. Cloud of Things enables in-network distributed processing of sensors data offered by the globally available IoT devices and provides a global platform for meaningful and responsive data analysis and decision making. We propose a distributed sensing resource discovery and virtualization algorithms that efficiently deploy virtual sensor networks on top of a subset of the selected IoT devices. We show, through analysis and simulations, the potential of the proposed solutions to realize virtual sensor networks with minimal physical resources, reduced communication overhead, and low complexity. We also design an uncoordinated, distributed algorithm that relies on the selected sensors to estimate a set of parameters without requiring synchronization among the sensors. Our simulations show that the proposed estimation algorithm, when compared to conventional alternating direction method of multipliers (ADMMs), reduces communication overhead significantly without compromising the estimation error. In addition, the convergence time, though increases slightly, is still linear as in the case of conventional ADMM.