Mobile phones might increase the severity of injuries sustained while being struck by lightning and doctors have advised patients to not use them outside during thunderstorms. Since it's advisable to not be outside (regardless of being on the phone or not) during a storm, it doesn't sound like bad advice.
Esprit and other doctors at the hospital added in a letter to the British Medical Journal that usually when someone is struck by lightning, the high resistance of the skin conducts the flash over the body in what is known as a flashover. But if a metal object, such as a phone, is in contact with the skin it disrupts the flashover and increases the odds of internal injuries and death.
Dangers attributed to mobile phones in the past include cancer and explosions.