A cutting element for a rotary drill bit that has a superabrasive member joined to a substrate at a three-dimensional interface is disclosed. The interface of the cutting element preferably incorporates a first ring pattern comprising a plurality of circumferentially arranged raised sections which are separated by a plurality of radially extending grooves. Also, the interface configuration may include at least a second ring pattern comprising a plurality of circumferentially arranged raised sections which are separated by a plurality of radially extending grooves. Radially adjacent ring patterns may substantially circumferentially overlap with one another. An interface of a cutting element including at least one ring pattern having an odd number of sections is also disclosed. Further, rotary drill bits including at least one such cutting element are disclosed.