Henrik Rung (31 March 1807 in Copenhagen – 12 December 1871 in the same place) was a Danish composer, singing teacher and conductor, father of Frederik and Georg Rung and Sophie Keller.
Rung was born in Copenhagen and moved to Næstved in September 1816, where he received guitar and violin lessons. In 1825, he returned to Copenhagen, where he received music theory lessons from C.E.F. Weyse, among others. In 1828, he became a double bass student at the Royal Chapel, and in 1834 he was appointed royal chapel musician.
In 1837, he received a travel grant to Italy, where he studied Italian vocal music and transcribed a large number of unpublished works from the Italian Renaissance. When he returned to Denmark, he became singing master at the Royal Theatre in 1842 and a much sought-after singing teacher.
In 1851, he founded the choral music association Cæciliaforeningen, of which he was chairman from 1851 to 1871. In 1862, he was made a Knight of the Order of Dannebrog and in 1866 a titular professor.
Rung was a prolific composer who wrote both operas and vocal pieces and the music for several hundred songs and romances. He is probably best known for I Danmark er jeg født (I was born in Denmark), but he also wrote the melodies for well-known hymns such as Kimer, I klokker! (Ring out, bells!), Alt står i Guds Faderhånd (All is in God’s Father’s hand) and Kirkeklokke, ej til Hovedstæder (Church bells, not for capitals).
He is buried in Holmens Kirkegård.