Lightning strikes can cause brief but strong voltage differentials, which will travel through wires and can destroy electric equipment, start fires, or even kill people in close contact with electrical equipment.
Snopes cites a number of examples of the latter: Lightning Telephone Deaths
This only applies to corded phones and other equipment connected by wire of course.
Although, standing outside in a thunderstorm while talking on a cellphone (or even just carrying one) can be bad for your health too. Like eletrical wiring, electronic devices too can act as "hot spots" for the sudden surge of electricity caused by lightning strikes. Snopes again: iFried