In most sexually reproducing animals, replication and maintenance of telomeres occurs in the germ line and during early development in embryogenesis through the use of telomerase. Somatic cells generally do not maintain telomere sequences, and these cells become senescent in adults as telomeres shorten to a critical length. Some animals reproduce clonally and must therefore require adult somatic mechanisms for maintaining their chromosome ends. Here we study the telomere biology of planarian flatworms with apparently limitless regenerative capacity fueled by a population of highly proliferative adult stem cells. We show that somatic telomere maintenance is different in asexual and sexual animals. Asexual animals maintain telomere length somatically during reproduction by fission or when regeneration is induced by amputation, whereas sexual animals only achieve telomere elongation through sexual reproduction. We demonstrate that this difference is reflected in the expression and alternate splicing of the protein subunit of the telomerase enzyme. Asexual adult planarian stem cells appear to maintain telomere length over evolutionary timescales without passage through a germ-line stage. The adaptations we observe demonstrate indefinite somatic telomerase activity in proliferating stem cells during regeneration or reproduction by fission, and establish planarians as a pertinent model for studying telomere structure, function, and maintenance.