COVID-19 affects a variety of organs and systems of the body including the central nervous system. Recent research has shown that COVID-19 survivors often experience neurological and psychological complications that can last for months after infection. We conducted a large internet study using online tests to analyze the effects of SARS-CoV-2 infection, COVID-19 severity, and vaccination on health, intelligence, memory, and information processing precision and speed in a cohort of 4,446 subjects. We found that both SARS-CoV-2 infection and COVID-19 severity were associated with negative impacts on patients' health. Furthermore, we observed a negative association between COVID-19 severity and cognitive performance. Younger participants had a higher likelihood of SARS-CoV-2 contraction, while the elderly had a higher likelihood of severe COVID-19 and vaccination. The association between age and COVID-19 severity was primarily mediated by older participants' impaired long-term health. Vaccination was positively associated with intelligence and the precision of information processing. However, the positive association between vaccination and intelligence was likely mediated by achieved education, which was itself strongly associated with the likelihood of being vaccinated.