In this paper, we argue that a broad range of large-scale network services would benefit from a scalable mechanism for delivering state about a random subset of global participants. Key to this approach is ensuring that membership in the subset changes periodically and with uniform representation over all participants. Random subsets could help overcome inherent scaling limitations to services that maintain global state and perform global network probing. It could further improve the routing performance of peer-to-peer distributed hash tables by locating topologically-close nodes. This paper presents the design, implementation, and evaluation of RanSub, a scalable protocol for delivering such state. As a first demonstration of the RanSub utility, we construct SARO, a scalable and adaptive application-layer overlay tree. SARO uses RanSub state information tolocate appropriate peers for meeting application-specific delay and bandwidth targets and to dynamically adapt to changing network conditions. A large-scale evaluation of 1000 overlay nodes participating in an emulated 20,000- node wide-area network topology demonstrate both the adaptivity and scalability (in terms of per-node state and network overhead) of both RanSub and SARO. Finally, we use an existing streaming media server to distribute content through SARO running on top of the PlanetLab Internet testbed.