An item such as a fabric-based item may have one or more input devices. The input devices may have terminals that are electrically coupled to control circuitry. The control circuitry may make resistance measurements, capacitance measurements, and other measurements on the input devices to determine whether the input devices have been pressed by a user's finger or have otherwise received input. The input devices may be used to form an array of switches for a keyboard, may form buttons on an electronic device housing or case, may be part of an item of clothing, or may be incorporated into other items such as fabric-based items. The input devices may have collapsible fabric structures such as collapsible fabric domes. The terminals of the input devices may be formed from conductive strands of material in the fabric domes or may be supported by other structures that buckle under applied pressure.