An electronic device may have a housing configured to be worn on a user's body or held in a user's hand. The electronic device may have control circuitry that wirelessly controls external equipment such as equipment with a display. By gathering motion information and other user input and wirelessly transmitting this information to the external equipment, the electronic device may serve as a wireless controller that controls content on the display. The electronic device may have multiple structures that move relative to each other such as first and second housing portions. The second housing portion may move to an extended position where the gathering of sensor information on changes in user finger position as the user interacts with real-world objects is enhanced.