A finger device may be worn on a user's finger and may serve as a controller for a head-mounted device or other electronic device. The finger device may have a housing having an upper housing portion that extends across a top of the finger and first and second side housing portions that extend down respective first and second sides of the finger. Sensors in the side housing portions may measure movements of the sides of the finger as the finger contacts an external surface. To ensure that the sensors are appropriately positioned relative to the sides of the finger, the housing may include one or more adjustable structures such as an elastomeric band, a drawstring, a ratchet mechanism, a scissor mechanism, and/or other adjustable structures for adjusting the position of the first and second side housing portions and associated sensors relative to the upper housing portion.