Background: South Korea has made substantial progress on tobacco control, but cigarette smoking prevalence is still high. Previous studies were conducted before the use of nicotine vaping products (NVPs) or heated tobacco products (HTPs) became popular. Thus, whether the concurrent use of NVPs or HTPs affects quit intentions among Korean smokers remains a question that needs to be explored. This study aims to identify predictors of quit intentions among cigarette-only smokers and concurrent users of cigarettes and NVPs or HTPs. Methods: Data were from the 2020 International Tobacco Control Korea Survey. Included in the analysis were 3778 adult cigarette smokers: 1900 at-least-weekly exclusive smokers and 1878 at-least-weekly concurrent smokers and HTP or NVP users. Bivariate and multivariable logistic regression analyses were conducted. Results: Quit intentions were reported by 66.4% of respondents. Factors significantly associated with quit intentions included younger age, having a spouse/partner, lower nicotine dependence, reporting a past quit attempt, regretting starting smoking, believing that smoking had damaged health, worrying that smoking will damage future health, and perceiving health benefits of quitting. Current use of NVPs or HTPs was not significantly associated with quit intentions. Conclusions: This study contributes the following to current literature: intrinsic health-related beliefs were more important than societal norms in shaping quit intentions. These findings should be considered in shaping future smoking cessation policies, such as reinforcing education programs that emphasize the benefits of quitting for personal health reasons, lowering nicotine dependence, and encouraging multiple quit attempts and successful quitting.