Why am I getting shocked by my iPhone headphones?

Static electricity buildup is causing your headphones to discharge small amounts of electricity into your ears. This is more likely to happen in a dry environment.

The electrostatic buildup occurs in the device and is discharged through the earbuds connected to the iPhone or iPod. Although harmless, this can be uncomfortable.

Static buildup can occur for several reasons:

A low humidity (dry) environment.
A very windy environment.
Moving the iPhone in and out of a pocket.
Synthetic fibers such as nylon are easily charged.
Jogging or exercising with the iPhone.

To alleviate the problem, touch an unpainted, grounded metal object before putting on the headphones. According to Apple, there are also other ways to reduce static electricity:

Indoors
Try raising the moisture level in the air of the local environment by using a portable humidifier or adjusting the humidity control on your air conditioner.

There are a number of anti-static sprays that can be sprayed into the air that can be used to reduce static.

If you have dry skin, try anti-static hand lotion.

Try wearing different clothes. Try clothes with natural fibers since synthetic fibers are more likely to hold a static charge.

Outdoors
Try to keep your device out of the wind by using a case, or leaving it in your bag or pocket.

Avoid removing your device from your pockets frequently as rubbing the device on certain materials can cause a static build up.