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We present observations of the early X-ray emission for a sample of 40 gamma-ray bursts (GRBs) obtained using the Swift satellite, for which the narrow-field instruments were pointed at the burst within 10 minutes of the trigger. Using data from the Burst Alert Telescope and the X-Ray Telescope, we show that the X-ray light curve can be well described by an exponential that relaxes into a power law, often with flares superimposed. The transition time between the exponential and the power law provides a physically defined timescale for the burst duration. In most bursts, the power law breaks to a shallower decay within the first hour, and a late emission" hump" is observed, which can last for many hours. In other GRBs the hump is weak or absent. The observed variety in the shape of the early X-ray light curve can be explained as a combination of three components: prompt emission from the central engine, afterglow …