Several preventive measures have been applied to limit the COVID-19 pandemic, including successful the development and introduction of vaccines. The aim of this study was to investigate adherence to preventive measures and vaccination intentions among nursing students in three European countries and the factors associated with vaccination intention and advising vaccination. A cross-sectional study using convenience/snow-ball sampling strategy was performed in Slovenia, Poland, and Serbia between 12 February and 5 March 2021. Data from 872 eligible respondents were analyzed (mean age 23.5 ± 6.5 years, 89% female). Higher adherence to preventive behavior was declared by those working in healthcare (p < 0.001), engaged in COVID-19 departments (p < 0.001), had not had the disease yet (p < 0.001), and had children (p = 0.01). Those groups also expressed higher vaccination intention and advised vaccination to others. Higher vaccination intention and advising vaccination were mostly associated with belief in benefits of vaccine, trust in institutions, perceived effectiveness of vaccine, influence of social environment, protection of patients and perceived health care professionals’ duty. Fear of side effects and general refusal of vaccines are the main reasons for vaccination hesitancy. The results of the study indicate how higher education institutions can support the development of appropriate professional attitudes and behaviors among nursing students.