Twitter does not impose a Real-Name policy for usernames, giving users the freedom to choose how they want to be identified. This results in some users being Identifiable (disclosing their full name) and some being Anonymous (disclosing neither their first nor last name). In this work we perform a large-scale analysis of Twitter to study the prevalence and behavior of Anonymous and Identifiable users. We employ Amazon Mechanical Turk (AMT) to classify Twitter users as Highly Identifiable, Identifiable, Partially Anonymous, and Anonymous. We find that a significant fraction of accounts are Anonymous or Partially Anonymous, demonstrating the importance of Anonymity in Twitter. We then select several broad topic categories that are widely considered sensitive-including pornography, escort services, sexual orientation, religious and racial hatred, online drugs, and guns-and find that there is a correlation between content sensitivity and a user's choice to be anonymous. Finally, we find that Anonymous users are generally less inhibited to be active participants, as they tweet more, lurk less, follow more accounts, and are more willing to expose their activity to the general public. To our knowledge, this is the first paper to conduct a large-scale data-driven analysis of user anonymity in online social networks.