We have assembled a sample of 1187 thermonuclear ( type-I ) X-ray bursts from observations of 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 ( confirmed via comparisons with numerical models ) 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 in general 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 ) , and calculated the mean burst rate as a function of accretion rate for the two groups . The decrease in burst rate observed at > 0.06 \dot { M } _ { Edd } ( \gtrsim 2 \times 10 ^ { 37 } { erg s ^ { -1 } } ) 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 many examples of bursts with recurrence times < 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 spinning 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 alternatively that the nature of the mass donor ( and hence the evolutionary history ) has an influence on the long-term spin evolution .