Sodankylä, which is located at 67° 25' N, 26° 35' E: Today, the Sun will set twice! Since the first sunset after the end of the Polar Day on 14th July 2012, the "nights" have been so short that, due to the Daylight Saving Time, the sunset happened after midnight and the sunrise soon afterwards. Today, on Friday, 20th July 2012, "yesterday's" Sun will set at 00:05 hrs, i.e. just after midnight of the new calendar day. Then the sun will rise again for the new day at 02:36 hrs. In between it will not get dark at all, because the Sun will only dip very little below the northern horizon.
As the nights are getting longer now by about 14 min per day, "today's" sunset will not anymore be after midnight, but it will happen on the same day, at 23:58 hrs. Therefore, today there will be two sunsets, one at 00:05 hrs, and one at 23:58 hrs.
Photo of sunset by Thomas Ulich.