Known as "KR," they play in black and white striped shirts, reportedly adopted from Newcastle. They won their first title in 1912, then won it again in 1919. A relative dry spell followed before they picked up another title in 1926, but they dominated the league afterward, winning six of the next eight.
KR fell off a bit in the latter half of the twentieth century, failing to win a single title in the Seventies or Eighties, and winning only one--the 1999 championship--in the Nineties. But that sparked another run of success that led to their record 25th title in 2011. It was part of a double that season that also include their record 12th Icelandic Cup.
They originally chose the name "Fótboltafélag Reykjavíkur," which apparently translates as "Reykjavik Football Club," but soon exchanged the prefix for Knattspyrnufélag, which (I am told) literally translates as "ball kickers."