Icelandic league saw it's first season in 1912. Since then KR has won it 26 times. They like to pride themselves on that however it's not that impressive when you look into it. For the first 13 seasons there were only 3 teams with 2 games each (once KR even played twice whilst the match between the other two teams got cancelled).
The right count, IMO, would be to start count int 1959. 6 teams and each team played each other twice. 10 games in total. A big step up from 5 games the previous season. If we start count there then ÍA has the most titles with 13.
Another milestone is 1977 when the league first had 10 competitors. It stayed that way until 2008 when the leagues got changed from 10 to 12 teams each.