We present the first systematic investigation of the morphological and timing properties of flares in GRBs observed by Swift/XRT. We consider a large sample drawn from all GRBs detected by Swift, INTEGRAL and HETE-2 prior to 2006 Jan 31, which had an XRT follow-up and which showed significant flaring. Our sample of 33 GRBs includes long and short, at low and high redshift, and a total of 69 flares. The strongest flares occur in the early phases, with a clear anti-correlation between the flare peak intensity and the flare time of occurrence. Fitting each X-ray flare with a Gaussian model, we find that the mean ratio of the width and peak time is <Delta t / t > = 0.13+/-0.10, albeit with a large scatter. Late flares at times > 2000 seconds have long durations, Delta t>300 s, and can be very energetic compared to the underlying continuum. We further investigated if there is a clear link between the number of pulses detected in the prompt phase by BAT and the number of X-ray flares detected by XRT, finding no correlation. However, we find that the distribution of intensity ratios between successive BAT prompt pulses and that between successive XRT flares is the same, an indication of a common origin for gamma-ray pulses and X-ray flares. All evidence indicates that flares are indeed related to the workings of the central engine and, within the standard fireball scenario, originate from internal shocks rather than external shocks. While all flares can be explained by long-lasting engine activity, 29/69 flares may also be explained by refreshed shocks. However, 10 can only be explained by prolonged activity of the central engine.
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