Overlay networks are a key vehicle for delivering network and processing resources to high performance applications. For shared networks, however, to consistently deliver such resources at desired levels of performance, overlays must be managed at runtime, based on the continuous assessment and prediction of available distributed resources. Data-intensive applications, for example, must assess, predict, and judiciously use available network paths, and dynamically choose alternate or exploit concurrent paths. Otherwise, they cannot sustain the consistent levels of performance required by tasks like remote data visualization, online program steering, and remote access to high end devices. The multiplicity of data streams occurring in complex scientific workflows or in large-scale distributed collaborations exacerbate this problem, particularly when different streams have different performance requirements. This paper presents IQ-Paths, a set of techniques and their middleware realization that implement self-regulating overlay streams for data-intensive distributed applications. Self-regulation is based on (1) the dynamic and continuous assessment of the quality of each overlay path, (2) the use of online network monitoring and statistical analyses that provide probabilistic guarantees about available path bandwidth, loss rate, and RTT, and (3) self-management, via an efficient packet routing and scheduling algorithm that dynamically schedules data packets to different overlay paths in accordance with their available bandwidths. IQ-Paths offers probabilistic guarantees for application-level specifications of stream utility, based on statistical predictions of available network bandwidth. This affords applications with the ability, for instance, to send control or steering data across overlay paths that offer strong guarantees for future bandwidth vs. across less guaranteed paths. Experimental results presented in this paper use IQ-Paths to better handle the different kinds of data produced by two high performance applications and one multimedia application: (1) a data-driven interactive high performance code with user-defined utility requirements, (2) an adaptive overlay version of the popular Grid-FTP application, and (3) a MPEG-4 Fine-Grained Scalable layered video streaming.