Positron Emission Tomography (PET) is a powerful molecular imaging tool that plays a crucial role in modern medical diagnostics by visualizing radio-tracer distribution to reveal physiological processes. Accurate organ segmentation from PET images is essential for comprehensive multi-systemic analysis of interactions between different organs and pathologies. Existing segmentation methods are limited by insufficient annotation data and varying levels of annotation, resulting in weak generalization ability and difficulty in clinical application. Recent developments in segmentation foundation models have shown superior versatility across diverse segmentation tasks. Despite the efforts of medical adaptations, these works primarily focus on structural medical images with detailed physiological structural information and exhibit limited generalization performance on molecular PET imaging. In this paper, we collect and construct PETS-5k, the largest PET segmentation dataset to date, comprising 5,731 three-dimensional whole-body PET images and encompassing over 1.3M 2D images. Based on the established dataset, we develop SegAnyPET, a modality-specific 3D foundation model for universal promptable segmentation from PET images. To issue the challenge of discrepant annotation quality, we adopt a cross prompting confident learning (CPCL) strategy with an uncertainty-guided self-rectification process to robustly learn segmentation from high-quality labeled data and low-quality noisy labeled data for promptable segmentation. Experimental results demonstrate that SegAnyPET can segment seen and unseen target organs using only one or a few prompt points, outperforming state-of-the-art foundation models and task-specific fully supervised models with higher accuracy and strong generalization ability for universal segmentation. As the first foundation model for PET images, we believe that SegAnyPET will advance the applications to various downstream tasks for molecular imaging.