Modern clinical databases include time series of vital signs, which are often recorded continuously during a hospital stay. Over several days, these recordings may yield many thousands of samples. In this work, we explore the feasibility of characterizing the state of health of a patient using the physiological dynamics inferred from these time series. The ultimate objective is to assist clinicians in allocating resources to high-risk patients. We hypothesize that similar patients exhibit similar dynamics and the properties and duration of these states are indicative of health and disease. We use Bayesian nonparametric machine learning methods to discover shared dynamics in patients' blood pressure (BP) time series. Each such dynamic captures a distinct pattern of evolution of BP and is possibly recurrent within the same time series and shared across multiple patients. Next, we examine the utility of this low-dimensional representation of BP time series for predicting mortality in patients. Our results are based on an intensive care unit (ICU) cohort of 480 patients (with 16% mortality) and indicate that the dynamics of time series of vital signs can be an independent useful predictor of outcome in ICU.