Quadruplex structures have been identified in a plethora of organisms where they play important functions in the regulation of molecular processes, and hence have been proposed as therapeutic targets for many diseases. In this paper we report the extensive bioinformatic analysis of the SARS-CoV-2 genome and related viruses using an upgraded version of the open-source algorithm G4-iM Grinder. This version improves the functionality of the software, including an easy way to determine the potential biological features affected by the candidates found. The quadruplex definitions of the algorithm were optimized for SARS-CoV-2. Using a lax quadruplex definition ruleset, which accepts amongst other parameters two residue G- and C-tracks, 512 potential quadruplex candidates were discovered. These sequences were evaluated by their in vitro formation probability, their position in the viral RNA, their uniqueness and their conservation rates (calculated in over seventeen thousand different COVID-19 clinical cases and sequenced at different times and locations during the ongoing pandemic). These results were then compared subsequently to other Coronaviridae members, other Group IV (+)ssRNA viruses and the entire viral realm. Sequences found in common with other viral species were further analyzed and characterized. Sequences with high scores unique to the SARS-CoV-2 were studied to investigate the variations amongst similar species. Quadruplex formation of the best candidates were then confirmed experimentally. Using NMR and CD spectroscopy, we found several highly stable RNA quadruplexes that may be suitable therapeutic targets for the SARS-CoV-2.