Future microprocessors increasingly rely on an unreliable CMOS fabric due to aggressive scaling of voltage and frequency, and shrinking design margins. Fortunately, many emerging applications can tolerate computational errors caused by hardware unreliabilities, at least during certain execution intervals. In this paper, we propose scalable stochastic processors, a computing platform for error-tolerant applications that is able to scale gracefully according to performance demands and power constraints while producing outputs that are, in the worst case, stochastically correct. Scalability is achieved by exposing to the application layer multiple functional units that differ in their architecture but share functionality. A mobile video encoding application here is able to achieve the lowest power consumption at any bitrate demand by dynamically switching between functional-unit architectures.