Observing the close relationship among panoptic, semantic and instance segmentation tasks, we propose to train a universal multi-dataset multi-task segmentation model: DaTaSeg. We use a shared representation (mask proposals with class predictions) for all tasks. To tackle task discrepancy, we adopt different merge operations and post-processing for different tasks. We also leverage weak-supervision, allowing our segmentation model to benefit from cheaper bounding box annotations. To share knowledge across datasets, we use text embeddings from the same semantic embedding space as classifiers and share all network parameters among datasets. We train DaTaSeg on ADE semantic, COCO panoptic, and Objects365 detection datasets. DaTaSeg improves performance on all datasets, especially small-scale datasets, achieving 54.0 mIoU on ADE semantic and 53.5 PQ on COCO panoptic. DaTaSeg also enables weakly-supervised knowledge transfer on ADE panoptic and Objects365 instance segmentation. Experiments show DaTaSeg scales with the number of training datasets and enables open-vocabulary segmentation through direct transfer. In addition, we annotate an Objects365 instance segmentation set of 1,000 images and release it as a public evaluation benchmark on https://laoreja.github.io/dataseg.