We examined how the thoughts, feelings, and behaviors of 6,957 students from Germany, assessed between March 16 and April 21, 2020, when COVID-19 became a serious health concern in Germany, varied by personality. The Big Five personality traits—openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability—were assessed with the International Personality Item Pool. Students were asked whether they kept up with the COVID-19 news, followed specific governmental rules and recommendations (washing hands more, using public transport less, avoiding larger crowds, and restricting meetings with family/friends), hoarded supplies, felt less secure in public places, or expected financial losses due to the crisis. Logistic regressions adjusted for sociodemographic factors and cognitive abilities revealed that more conscientious (odds ratio (OR) = 1.133) and more agreeable (OR = 1.285) students kept up with the news more. More agreeable students were also more likely to wash their hands more often/intensively (OR = 1.262), use public transport less (OR = 1.182), avoid crowds (OR = 1.320), and restrict meetings with family/friends (OR = 1.410). Other Big Five traits were not associated with these behaviors, except that less emotionally stable individuals tended to use public transport less often (OR = 1.162). Additionally, less emotionally stable students, in particular, more often bought more supplies than usual (OR = 1.322), felt insecure in public spaces (OR = 1.597), and expected financial losses (OR = 1.270). Moreover, less open (OR = 0.876) and more conscientious (OR = 1.235) students more often felt insecure in public spaces, and more extraverted individuals more often expected financial losses (OR = 1.180). Taken together, our findings suggest that more agreeable individuals, in particular, tend to comply with governmental rules and recommendations to fight COVID-19, whereas less emotionally stable individuals, in particular, tend to hoard supplies, feel insecure, and fear financial losses due to the crisis.