General:
* Headphones
* Earbuds
* Headsets
* Audio receivers
* Personal listening devices
Specific Types:
* In-ear monitors (IEMs): Used by musicians and audiophiles for high fidelity sound
* Over-ear headphones: Cover the entire ear
* On-ear headphones: Rest on the ear
* Bone conduction headphones: Transmit sound through vibrations against the cheekbone
* Wireless headphones: Connect via Bluetooth or other wireless technology
Informal:
* Buds
* Cans
* Earpieces
The best word to use depends on the specific context and the type of earphones you are referring to.