Robert William Otto Allen (18 March 1852 – 9 December 1888) was a Danish pianist, composer and conductor.
He was the brother of conductor Georg Frederik Ferdinand Allen.
He trained at the Royal Academy of Music as a student of Edmund Neupert.
From the late 1870s he was a music teacher in Aarhus and in 1885 he became organist at Ã…rhus Cathedral.
He was a frequent contributor to the Aarhus music scene both as a pianist, as conductor and as a composer.
Notable compositions include Koncertouverture i G-Dur (1881), Ouverture til Dina (1886) and Løft dit hoved, du raske gut (1883).