The detection of repeated subsequences, time series motifs, is a problem which has been shown to have great utility for several higher-level data mining algorithms, including classification, clustering, segmentation, forecasting, and rule discovery. In recent years there has been significant research effort spent on efficiently discovering these motifs in static offline databases. However, for many domains, the inherent streaming nature of time series demands online discovery and maintenance of time series motifs. In this paper, we develop the first online motif discovery algorithm which monitors and maintains motifs exactly in real time over the most recent history of a stream. Our algorithm has a worst-case update time which is linear to the window size and is extendible to maintain more complex pattern structures. In contrast, the current offline algorithms either need significant update time or require very costly pre-processing steps which online algorithms simply cannot afford. Our core ideas allow useful extensions of our algorithm to deal with arbitrary data rates and discovering multidimensional motifs. We demonstrate the utility of our algorithms with a variety of case studies in the domains of robotics, acoustic monitoring and online compression.