Light Detection and Ranging (LiDAR) sensors emit laser signals to calculate distances based on the time delay of the returned laser pulses. They can generate dense point clouds to map forest structures at a high level of spatial resolution. In this work, we consider the problem of segmenting out individual trees in Airborne Laser Scanning (ALS) point clouds. Several techniques have been proposed for this purpose which generally require time-consuming parameter tuning and intense user interaction. Our goal is to design an automated, intuitive, and robust approach requiring minimal user interaction. To this aim, we define a new segmentation approach based on topological tools, namely on the watershed transform and on persistence-based simplification. The approach follows a divide-and-conquer paradigm, splitting a LiDAR point cloud into regions with uniform densities. Our algorithm is validated on coniferous forests collected in the NEW technologies for a better mountain FORest timber mobilization (NEWFOR) dataset, and deciduous forests collected in the Smithsonian Environmental Research Center (SERC) dataset. When compared to four state-of-the-art tree segmentation algorithms, our method performs best in both ecosystem types. It provides more accurate stem estimations and single tree segmentation results at various of stem and point densities. Also, our method requires only a single (Boolean) parameter, which makes it extremely easy to use and very promising for various forest analysis applications, such as biomass estimation and field inventory surveys.