Identifying the worries of individuals and societies plays a crucial role in providing social support and enhancing policy decision-making. Due to the popularity of social media platforms such as Twitter, users share worries about personal issues (e.g., health, finances, relationships) and broader issues (e.g., changes in society, environmental concerns, terrorism) freely. In this paper, we explore and evaluate a wide range of machine learning models to predict worry on Twitter. While this task has been closely associated with emotion prediction, we argue and show that identifying worry needs to be addressed as a separate task given the unique challenges associated with it. We conduct a user study to provide evidence that social media posts express two basic kinds of worry – normative and pathological – as stated in psychology literature. In addition, we show that existing emotion detection techniques underperform, especially while capturing normative worry. Finally, we discuss the current limitations of our approach and propose future applications of the worry identification system.