Attenuation of seismic waves in the crust and the upper mantle has been studied in three global rift systems: the Baikal rift system (Eurasia), the North Tanzanian divergence zone (Africa) and the Basin and Range Province (North America). Using the records of direct and coda waves of regional earthquakes, the single scattering theory [Aki, Chouet, 1975], the hybrid model from [Zeng, 1991] and the approach described in [Wennerberg, 1993], we estimated the seismic quality factor (QC), frequency parameter (n), attenuation coefficient (delta), and total attenuation (QT). In addition, we evaluated the contributions of two components into total attenuation: intrinsic attenuation (Qi), and scattering attenuation (Qsc). Values of QC are strongly dependent on the frequency within the range of 0.2-16 Hz, as well as on the length of the coda processing window. The observed increase of QC with larger lengths of the coda processing window can be interpreted as a decrease in attenuation with increasing depth. Having compared the depth variations in the attenuation coefficient (delta) and the frequency (n) with the velocity structures of the studied regions, we conclude that seismic wave attenuation changes at the velocity boundaries in the medium. Moreover, the comparison results show that the estimated variations in the attenuation parameters with increasing depth are considerably dependent on utilized velocity models of the medium. Lateral variations in attenuation of seismic waves correlate with the geological and geophysical characteristics of the regions, and attenuation is primarily dependent on the regional seismic activity and regional heat flow. The geological inhomogeneities of the medium and the age of crust consolidation are secondary factors. Our estimations of intrinsic attenuation (Qi) and scattering attenuation (Qsc) show that in all the three studied regions, intrinsic attenuation is the major contributor to total attenuation. Our study shows that the characteristics of seismic wave attenuation in the three different rift systems are consistent with each other, and this may suggest that the lithosphere in the zones of these different rift systems has been modified to similar levels.