Background: In 2020, in 27 European Union (EU) Member States, melanoma accounted for 4% of all new cancer cases and 1.3% of all cancer deaths, making melanoma the fifth most common malignancy and placing it in the 15 most frequent causes of cancer deaths in the EU-27. The main aim of our study was to investigate melanoma mortality trends in 25 EU Member States and three non-EU countries (Norway, Russia, and Switzerland) in a broad time perspective (1960–2020) in a younger (45–74 years old) vs. older age group (75+). Methods: We identified melanoma deaths defined by ICD-10 codes C-43 for individuals aged 45–74 and 75+ years old between 1960–2020 in 25 EU Member States (excluding Iceland, Luxembourg, and Malta) and in 3 non-EU countries—Norway, Russia, and Switzerland. Age-standardized melanoma mortality rates (ASR) were computed using the direct age-standardization for Segi’s World Standard Population. To determine melanoma-mortality trends with 95% confidence intervals (CI), Joinpoint regression was applied. Our analysis used the Join-point Regression Program, version 4.3.1.0 (National Cancer Institute, Bethesda, MD, USA). Results: Regardless of the considered age groups, in all investigated countries, in general, melanoma standardized mortality rates were higher for men than women. Considering the age group 45–74, the highest number of countries was characterized by decreasing melanoma-mortality trends in both sexes—14 countries. Contrarily, the highest representation of countries in the age group 75+ was connected with increasing melanoma-mortality trends in both sexes—26 countries. Moreover, considering the older age group—75+—there was no country with a decreasing melanoma mortality in both sexes. Conclusions: Investigated melanoma-mortality trends vary in individual countries and age groups; however, a highly concerning phenomenon—increasing melanoma-mortality rates in both sexes—was observed in 7 countries for the younger age group and in as many as 26 countries for the older age group. There is a need for coordinated public-health actions to address this issue.