The United States once set off a nuke in space to see what would happen.

The test was called Starfish Prime, part of a series of tests known as Operation Fishbowl. The nuke's explosion took place 250 miles above a point 19 miles southwest of Johnston Island in the Pacific Ocean, on 8 July 1962, at 11:00 pm Honolulu time. 

The missile Thor, which was carrying the Starfish Prime nuke, reached a height of 680 miles, and the nuke was detonated after falling downward to 250 miles, 13 minutes and 41 seconds after liftoff. 

The interesting part was the effect of the electromagnetic pulse that happened as a result. It was so much larger than expected that it knocked most of the instruments way off scale, which forced 27 rockets to be fired later to obtain data because of how difficult it was to obtain. 

Additionally, there was electrical damage in Hawaii, almost 900 miles from the detonation point. About 300 streetlights were blown out, numerous burglar alarms were set off, and a telephone company's microwave link was damaged. As a result, telephone calls from Kauai to the other Hawaiian Islands were shut down. 

After the Starfish Prime detonation, bright auroras were seen in the sky surrounding the detonation area as well as on the opposite side of the equator, interestingly enough. A report claimed it could be seen all the way from Tongatapu to the French Frigate Shoals. For a few days after the burst, during twilight, the light particles from the blast illuminated the image of debris in the atmosphere. 

(Source)