Space-air-ground integrated network (SAGIN) has emerged as a paradigm shifting architecture that offers large-scale, flexible wireless coverage and seamless, high-rate connectivity to complement terrestrial communications. Nonetheless, unlocking the potentials of SAGIN is subject to addressing non-trivial challenges associated with their inherent time-variability, self-organization, and heterogeneity. Meanwhile, the concept of reconfigurable intelligent surfaces (RISs) is recognized as a disruptive technology that supports an unprecedented control of electromagnetic waves propagation and potentially offers significant enhancements in spectral efficiency, coverage expansion, and security, all achieved in a low-cost and energy-efficient manner. We anticipate that the integration of RISs into SAGIN will not only play a fundamental role in improving the quality of inter- and intra- layer communications, but will also provide complex interactions among the three network segments, and hence, opens the horizons for a new breed of applications across all industries. In this article, we explore the underlying opportunities and challenges of integrating RIS-enabled communications into SAGIN, and present a forward-looking overview of the cross-layer operational elements supported by RISs. Finally, we outline major enabling technologies and present a look ahead toward addressing open research issues.