The use of generative AI (GAI) among university students is rapidly increasing, yet empirical research on students' GAI use and the factors influencing it remains limited. To address this gap, we surveyed 363 undergraduate and graduate students in the United States, examining their GAI usage and how it relates to demographic variables and personality traits based on the Big Five model (i.e., extraversion, agreeableness, conscientiousness, and emotional stability, and intellect/imagination). Our findings reveal: (a) Students in higher academic years are more inclined to use GAI and prefer it over traditional resources. (b) Non-native English speakers use and adopt GAI more readily than native speakers. (c) Compared to White, Asian students report higher GAI usage, perceive greater academic benefits, and express a stronger preference for it. Similarly, Black students report a more positive impact of GAI on their academic performance. Personality traits also play a significant role in shaping perceptions and usage of GAI. After controlling demographic factors, we found that personality still significantly predicts GAI use and attitudes: (a) Students with higher conscientiousness use GAI less. (b) Students who are higher in agreeableness perceive a less positive impact of GAI on academic performance and express more ethical concerns about using it for academic work. (c) Students with higher emotional stability report a more positive impact of GAI on learning and fewer concerns about its academic use. (d) Students with higher extraversion show a stronger preference for GAI over traditional resources. (e) Students with higher intellect/imagination tend to prefer traditional resources. These insights highlight the need for universities to provide personalized guidance to ensure students use GAI effectively, ethically, and equitably in their academic pursuits.