Robots can better interact with humans and unstructured environments through touch sensing. However, most commercial robots are not equipped with tactile skins, making it challenging to achieve even basic touch-sensing functions, such as contact localization. We present UniTac, a data-driven whole-body touch-sensing approach that uses only proprioceptive joint sensors and does not require the installation of additional sensors. Our approach enables a robot equipped solely with joint sensors to localize contacts. Our goal is to democratize touch sensing and provide an off-the-shelf tool for HRI researchers to provide their robots with touch-sensing capabilities. We validate our approach on two platforms: the Franka robot arm and the Spot quadruped. On Franka, we can localize contact to within 8.0 centimeters, and on Spot, we can localize to within 7.2 centimeters at around 2,000 Hz on an RTX 3090 GPU without adding any additional sensors to the robot. Project website: https://ivl.cs.brown.edu/research/unitac.