The increased concentrations of greenhouse gases have led to global warming and an increased frequency and intensity of extreme weather events. Such changes in weather patterns may have unexpected implications for everyday life and water resource management in coastal and inland areas; thus, it is critical to understand the pattern of the changes. This study investigated how extreme weather events have changed in inland and coastal South Korea in the past 60 years (1961–2020) at different temporal scales, from monthly to yearly. This study quantified extreme weather events using multiple meteorological indices such as consecutive dry days (CDD), consecutive wet days (CWD), tropical nights, and icy and frosty days. The trends in the extreme weather indices were statistically tested using a non-parametric test. The results showed increases in the minimum and maximum air temperature and the frequency of warm and cold nights and days. The number of CDD and maximum five-day precipitation (RX5day) at the coastal and inland stations increased in the extreme precipitation-related index. The number of warm days and warm nights increased significantly at the majority of weather stations over the 60 year study period. The number of CWD increased during the selected period, but this was not statistically significant. In addition, we found that the temporal variations in the indices became greater over time, which implies the frequency and severity of extreme events such as drought and storm events may increase in the future. This study could help researchers determine the climatic areas at the selected stations that are critical for optimal water resource management planning and/or modeling.