Electronic devices with drop protection

A head-mounted device may include optical assemblies for presenting images to a user. Actuators may be used to adjust the spacing between the optical assemblies to accommodate different interpupillary distances. Upon detection of a power-down event or drop event, the device may be placed into an impact-safe mode. During the safe mode, the optical assemblies may be moved to predetermined impact-safe positions, brakes such as optical guide rail brakes may be adjusted, cushioning springs may be deployed, clutches may be adjusted, and/or other safety mechanisms may be activated to help protect the optical assemblies or other sensitive components from damage.