Even though most states don't restrict wearing headphones while driving, doing so is antithetical to basic road safety. One of the most important parts of driving is being aware of your surroundings, both visually and sonically. Wearing headphones while driving — especially if you cover both ears — severely hinders your ability to hear things like sirens, approaching cars and honks.
Aside from the danger, driving while using headphones also puts you at risk legally, even if the activity itself isn't outright banned. It can be classified by law enforcement as distracted or even reckless driving if it hinders your ability on the road, and if you get into an accident while wearing headphones, you can be opened up to a lawsuit whether you were at fault or not. Driving with headphones can be viewed as negligence, even with an accident you didn't cause. In a state with comparative or contributory negligence laws, you can be given a reduced financial payout — or none at all.
Almost every car is equipped with some kind of way to connect your music or phone calls to your speakers, whether it's a direct Bluetooth connection, AUX cord or USB port. If none of these options are available, it's still easily remedied with the purchase of an FM adapter, which can connect to your device and transmit your music and phone calls over the radio. At the end of the day, there's really no good reason to be driving with headphones on — the risks far outweigh any benefits.