In later generations, younger sons were "just" Princes of Denmark.
In modern times - as mentioned above - younger princes or their sons - tended to marry non-royals and being granted the title of Count of Rosenborg. Most of those counts and countesses have normal jobs (like the rest of the Danish nobles). Many expect the possible children of the present younger royals to become Counts af Montpezat.
In the 20th century younger unmarried royals tended to work with the military, and H.H. Princess Elisabeth was a senior clerk in the Foreign Ministry.