Timelines are essential for visually communicating chronological narratives and reflecting on the personal and cultural significance of historical events. Existing visualization tools tend to support conventional linear representations, but fail to capture personal idiosyncratic conceptualizations of time. In response, we built TimeSplines, a visualization authoring tool that allows people to sketch multiple free-form temporal axes and populate them with heterogeneous, time-oriented data via incremental and lazy data binding. Authors can bend, compress, and expand temporal axes to emphasize or de-emphasize intervals based on their personal importance; they can also annotate the axes with text and figurative elements to convey contextual information. The results of two user studies show how people appropriate the concepts in TimeSplines to express their own conceptualization of time, while our curated gallery of images demonstrates the expressive potential of our approach.