An electronic device may be coupled to an accessory such as a pair of earphones. The earphones may have multi-user sensor structures that determine whether or not the earphones are being shared by multiple users. The multi-user sensor structures may include an angle sensor configured to measure an angle at the Y-junction of a cable associated with the pair of headphones. When the first and second speakers are both located in the ears of a single user, the electronic device may perform functions such as playing audio content. When one of the speakers is located in an ear of a first user while the other of the speakers is located in an ear of a second user, the electronic device can automatically take actions such as switching from stereo to mono playback, playing a different type of audio content to each earphone, or other suitable action.