The promotion of healthful dietary intake in adolescents is an important public health concern, as obesity is on the rise among adolescents. The current study aimed to determine the association between sociodemographic characteristics and dietary intake (breakfast, vegetables, milk, fruits, fast food, carbohydrate beverages, and caffeine beverages) and to examine the influences of physical and mental health on dietary intake. A nationally representative sample of 187,622 adolescents who attended middle and high schools and participated in the Korean Youth Risk Behavior Survey (2015, 2017, and 2019) was used. The results showed a decrease in breakfast, vegetable, milk, and fruit consumption and an increase in the obesity rate from 2015 to 2019. There was a significant association between dietary intake and gender, economic status, BMI, and academic achievement. Multiple logistic regression analysis results revealed that the consumption of breakfast, vegetables, milk, and fruit were associated with greater odds of having enough sleep. Fast food intake was shown to be a significant risk factor for depression with an odds ratio of 1.204 (95% CI = 1.169–1.239), and carbonated beverage consumption was shown to be a significant risk factor for stress with an odds ratio of 1.042 (95% CI = 1.030–1.054). These results provide fundamental data that can be used to develop an effective nutrition intervention program or nutrition policy for adolescents or school food service programs.