Consolidation of workloads has emerged as a key mechanism to dampen the rapidly growing energy expenditure within enterprise-scale data centers. To gainfully utilize consolidation-based techniques, we must be able to characterize the power consumption of groups of co-located applications. Such characterization is crucial for effective prediction and enforcement of appropriate limits on power consumption---power budgets---within the data center. Power budgets need to be enforced at multiple spatial granularities within a data center: from server and rack to the room-level. Furthermore, power budgets must be also enforced at multiple temporal granularities: from durations of less than a second (dictated by fuses for reliability concerns) to longer periods of several minutes to hours (relevant to energy optimization considerations.) We capture these requirements in the form of two kinds of power budgets at each spatial level: (i) an average budget to capture an upper bound on long-term energy consumption within that level and (ii) a sustained budget to capture any restrictions on sustained draw of current above a certain threshold. Using a simple measurement infrastructure, we derive power profiles---statistical descriptions of the power consumption of applications. Based on insights gained from detailed profiling of several applications---both individual and consolidated---we develop models for predicting average and sustained power consumption of consolidated applications. We conduct an experimental evaluation of our techniques on a Xen-based server that consolidates applications drawn from a diverse pool. For a variety of consolidation scenarios, we are able to predict average power consumptions within 5% error-margin. Our sustained power prediction techniques allow us to predict close yet safe upper bounds on the sustained power consumption of consolidated applications.