An electronic device has circuitry mounted within an electronic device housing. The electronic device housing may have housing walls such as metal sidewalls. Openings are formed in an electronic device housing wall to accommodate buttons. A button may have a switch with a switch housing mounted to the housing wall. A movable button member that extends from the switch housing may protrude through a housing opening. Switch terminals are coupled to signal lines on structures such as flexible printed circuits. The switch terminals may be formed from portions of elongated switch leads supported by support structure that are mounted to the housing wall or may be formed on an inner surface of the switch housing. Support structures may be molded into engagement with features on a housing wall or may be mounted to a housing wall using a fastener such as a screw.