Spermatogonial stem cells (SSCs) propagate mammalian spermatogenesis throughout male reproductive life by continuously self-renewing and differentiating, ultimately, into sperm. SSCs can be cultured for long periods and restore spermatogenesis upon transplantation back into the native microenvironment in vivo. Conventionally, SSC research has been focused mainly on male infertility and, to a lesser extent, on cell reprogramming. With the advent of genome-wide sequencing technology, however, human studies have uncovered a wide range of pathogenic alleles that arise in the male germline. A subset of de novo point mutations (DNMs) was shown to originate in SSCs and cause congenital disorders in children. This review describes both monogenic diseases (e.g., Apert syndrome) and complex disorders that are either known or suspected to be driven by mutations in SSCs. We propose that SSC culture is a suitable model for studying the origin and mechanisms of these diseases. Lastly, we discuss strategies for future clinical implementation of SSC-based technology, from detecting mutation burden by sperm screening to gene correction in vitro.