Birth stories have become increasingly common on the internet, but they have received little attention as a computational dataset. These unsolicited, publicly posted stories provide rich descriptions of decisions, emotions, and relationships during a common but sometimes traumatic medical experience. These personal details can be illuminating for medical practitioners, and due to their shared structures, birth stories are also an ideal testing ground for narrative analysis techniques. We present an analysis of 2,847 birth stories from an online forum and demonstrate the utility of these stories for computational work. We discover clear sentiment, topic and persona-based patterns that both model the expected narrative event sequences of birth stories and highlight diverging pathways and exceptions to narrative norms. The authors' motivation to publicly post these personal stories can be a way to regain power after a surveilled and disempowering experience, and we explore power relationships between the personas in the stories, showing that these dynamics can vary with the type of birth (e.g., medicated vs unmedicated). Finally, birth stories exist in a space that is both public and deeply personal. This liminality poses a challenge for analysis and presentation, and we discuss tradeoffs and ethical practices for this collection. WARNING: This paper includes detailed narratives of pregnancy and birth.CCS Concepts: • Computing methodologies → Natural language processing; Discourse, dialogue and pragmatics.