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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 January 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 anticorrelation 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\langle\Delta t/t\rangle= 0.13\pm 0.10, albeit with a large scatter. Late flares at times> 2000 s have long durations,\Delta t> 300 s, and can be very energetic compared to the underlying continuum. We further investigated whether there is a clear link between the number of …