The designers at Studio Banana Things have newly released ear-free headphones, named BATBAND, which sit on the back of your head, rather than covering your ears.
Description from the designers: BATBAND is a beautiful piece of sound technology allowing you to listen to your own soundscape as well as the world that surrounds you. The human-centered design fits technology delivering high fidelity acoustic experience via an innovative bone conduction system. BATBAND works via bone conduction, consisting of transducers that transmit sound waves sensed by your inner ear, thus freeing your “social” outer ear.
https://www.kickstarter.com/projects/ostrich-pillow/batband