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EMPs (electro-magnetic pulses) occur naturally often.  Every lightning strike is one example.

Larger EMPs have been created artificially with nuclear weapons.  The Starfish Prime H-bomb test caused damage a long way away in Hawaii.  There were cases of the wires in street lights getting fused by the large pulse of induced current caused by the EMP.

Global EMP damage is quite unlikely, because the earth acts like a shield.  Some radiation can bounce between the ground and the ionosphere, and thereby propagate around the earth, but that is only over narrow wavelengths, and there is considerable attenuation in any case.  Assuming you're not considering events that are so energetic as to ionize the atmosphere or melt the surface, about half the earth's surface would be reasonably unscathed.  We're also assuming a "pulse", so the event is basically instantaneous relative to the rotation of the earth.

However, a global disaster resulting from a localized EMP effect is more possible.  Imagine every transistor in North America blown out.  That would have global repercussions, even if no electronic device were harmed in the rest of the world.