Until 1848, Denmark was an absolute monarchy. With the introduction of representative democracy, the monarch was no longer both the head of state and the head of government. The latter office now (gradually) devolved upon an elected official - a prime minister, though the title was altered several times.
Denmark underwent several constitutional changes in the century-and-a-half since then, and the title of the head of government was similarly changed, along the way. The following is a list of all the people who have held the office to date, with their titles. If a head of government held office for more than one successive term, then the beginning of each term is listed.
From March 1848, title: premier
From December 1855, title: konseilspræsident ("president of the privy council")
From April 1918, title: statsminister ("minister of state")
Related nodes: Monarchs of Denmark - Danish Myths and Legends