Problematic Internet Use (PIU) is a broad term that covers problems with Internet use that result in psychological, social, academic or professional difficulties. The aim of our study was to identify individuals particularly vulnerable to developing PIU among Polish students, taking into account sociodemographic characteristics and Internet use patterns. A total of 1008 students of Polish universities took part in the survey. The research tool was The Problematic Internet Use Test—the Polish version of the Internet Addiction Test. Among the respondents, 10.2% showed signs of PIU—high or very high risk of addiction. Significantly higher levels of PIU were found in males than females, science students than medical and humanities students, and Internet users using a computer, as opposed to students using only a phone/tablet. A decrease in PIU was observed as students improved their assessment of their material situation. The severity of PIU increased significantly as the importance of Internet use for entertainment increased. Our research indicates that it is worth implementing measures to prevent the development of PIU in Poland, e.g., screening educational campaigns, especially for science students. It is also necessary to offer students at lower levels of education, especially the less affluent, forms of leisure time other than computer activity with the use of the Internet.