Traditional GUI applications provide limited support for tangible interaction, as most applications are not programmed to support tangible input, and most input devices do not provide haptic feedback. To address this limitation, we introduce GUI Robots, a software framework that enables developers to repurpose off-the-shelf robots as tangible input and haptic output devices, and to connect them to unmodified desktop applications. We introduce the GUI Robots framework and present several proof-of-concept applications, including a haptic scroll wheel, force feedback game controllers, a 3D mouse, and a self-driving notification robot. To evaluate whether GUI Robots can be used to prototype tangible interfaces for existing applications, we conducted a user study in which developers created customized tangible interfaces for two applications. Study participants were able to create tangible user interfaces for these applications in less than an hour. GUI Robots allows developers to easily extend applications with tangible input and haptic output.