An electronic device such as an earbud may have control circuitry mounted in a housing. The housing may have portions such as an ear portion with a speaker port through which a speaker plays audio and a stalk portion that extends from the ear portion. Proximity sensors may be formed in the electronic device. For example, one or more proximity sensors may be formed on the ear portion to detect when a user has inserted an earbud into the ear of the user and/or one or more proximity sensors may be formed on a stalk portion to detect when a user is holding an earbud by the stalk or when a user is providing finger touch input such as taps, swipes, and/or other gestures on the stalk portion. The proximity sensors may be optical proximity sensors such as coherent self-mixing proximity sensors.