The current document is directed to systems and methods that stream real-time, processed data from remote processor-controlled user appliances, including personal computers, tablets, mobile phones, and laptops, to application programs for display, analysis, and other purposes and to other data-consuming devices and systems. In one implementation, a real-time processed-data streaming system includes instrumentation within remote, processor-controlled user devices, data collection at geographically distributed data-collection centers, consolidation of event messages generated by the geographically distributed data-collection centers within consolidation systems, processing of the consolidated event messages within one or more processing centers, and streaming of processed data, in the form of various types of processed-data-containing messages, to consumers of the data, including application programs that render the data for display on electronic display devices.