  Several gamma-ray bursts (GRBs) last much longer (~hours) in gamma-rays than
typical long GRBs (~ minutes), and recently it was proposed that these
"ultra-long GRBs" may form a distinct population, probably with a different
(e.g. blue supergiant) progenitor than typical GRBs. However, Swift
observations suggest that many GRBs have extended central engine activities
manifested as flares and internal plateaus in X-rays. We perform a
comprehensive study on a large sample of Swift GRBs with XRT observations to
investigate GRB central engine activity duration and to determine whether
ultra-long GRBs are unusual events. We define burst duration t_burst based on
both gamma-ray and X-ray light curves rather than using gamma-ray observations
alone. We find that t_burst can be reliably measured in 343 GRBs. Within this
"good" sample, 21.9% GRBs have t_burst >=10^3 s and 11.5% GRBs have t_burst
>=10^4 s. There is an apparent bimodal distribution of t_burst in this sample.
However, when we consider an "undetermined" sample (304 GRBs) with t_burst
possibly falling in the gap between GRB duration T_90 and the first X-ray
observational time, as well as a selection effect against t_burst falling into
the first Swift orbital "dead zone" due to observation constraints, the
intrinsic underlying t_burst distribution is consistent with being a single
component distribution. We found that the existing evidence for a separate
ultra-long GRB population is inconclusive, and further multi-wavelength
observations are needed to draw a firmer conclusion. We also discuss the
theoretical implications of our results. In particular, the central engine
activity duration of GRBs is generally much longer than the gamma-ray T90
duration and it does not even correlate with T90. It would be premature to make
a direct connection between T90 and the size of the progenitor star.
