  We have assembled a sample of 1187 thermonuclear (type-I) X-ray bursts from
48 accreting neutron stars by the Rossi X-ray Timing Explorer, spanning more
than ten years. The sample contains examples of two of the three theoretical
ignition regimes and likely examples of the third. We present a detailed
analysis of the variation of the burst profiles, energetics, recurrence times,
presence of photospheric radius expansion, and presence of burst oscillations,
as a function of accretion rate.
  We estimated the distance for 35 sources exhibiting radius-expansion bursts,
and found that the peak flux of such bursts varies typically by 13%. We
classified sources into two main groups based on the burst properties: both
long and short bursts (indicating mixed H/He accretion), and consistently short
bursts (primarily He accretion). The decrease in burst rate observed for both
groups at >0.06 Mdot_Edd (>~2E37 erg/s) is associated with a transition in the
persistent spectral state and (as has been suggested previously) may be related
to the increasing role of steady He-burning. We found examples of bursts
separated by <30 min, including burst triplets and even quadruplets.
  We describe the oscillation amplitudes for 13 of the 16 burst oscillation
sources, as well as the stages and properties of the bursts in which the
oscillations are detected. The burst properties are correlated with the burst
oscillation frequency; sources at <400 Hz generally have consistently short
bursts, while the more rapidly-spinning systems have both long and short
bursts. This correlation suggests either that shear-mediated mixing dominates
the burst properties, or that the nature of the mass donor (and hence the
evolutionary history) has an influence on the long-term spin evolution.
