Online users engage in self-disclosure - revealing personal information to others - in pursuit of social rewards. However, there are associated costs of disclosure to users' privacy. User profiling techniques support the use of contributed content for a number of purposes, e.g., micro-targeting advertisements. In this paper, we study self-disclosure as it occurs in newspaper comment forums. We explore a longitudinal dataset of about 60, 000 comments on 2202 news articles from four major English news websites. We start with detection of language indicative of various types of self-disclosure, leveraging both syntactic and semantic information present in texts. Specifically, we use dependency parsing for subject, verb, and object extraction from sentences, in conjunction with named entity recognition to extract linguistic indicators of self-disclosure. We then use these indicators to examine the effects of anonymity and topic of discussion on self-disclosure. We find that anonymous users are more likely to self-disclose than identifiable users, and that self-disclosure varies across topics of discussion. Finally, we discuss the implications of our findings for user privacy.