Raff was born in Lachen in Switzerland. He was largely self-taught in music, studying the subject while working as a schoolmaster. He sent some of his piano compositions to Felix Mendelssohn who recommended them to Breitkopf and Härtel for publication. They were published in 1844 and received a favourable review in Robert Schumann's journal, the Neue Zeitschrift für Musik, which prompted Raff to go to Zürich and take up composition full time.
In 1845, Raff walked to Basel to hear Franz Liszt play the piano. After a period in Stuttgart where he became friends with the conductor Hans von Bülow, he worked as Liszt's assistant at Weimar from 1850 to 1855. During this time he helped the Hungarian in the orchestration of several of his works, claiming to have had a particularly big part in orchestrating the symphonic poem Tasso. In 1851, Raff's opera König Alfred was staged in Weimar, and five years later he moved to Wiesbaden where he largely devoted himself to composition. From 1877 he was a teacher at, and administrator of, the Hoch Conservatory in Frankfurt am Main. There he employed Clara Schumann and a number of other women as teachers, and established a class specifically for female composers (this was at a time when women composers were not taken very seriously). His pupils there included Edward MacDowell and Alexander Ritter. He died in Frankfurt am Main.
Raff was very prolific, and by the end of his life was one of the best known German composers, though his work is largely forgotten today (the only one of his pieces received anything like regular performance today is a cavatina for violin and piano, sometimes played as an encore). He drew influence from a variety of sources - his eleven symphonies, for example, combine the Classical symphonic form, with the Romantic penchant for programme music and contrapuntal orchestral writing which harks back to the Baroque. Several of these symphonies carry descriptive titles including In the Forest (number three), Lenore (number five) and To the Fatherland (number one), a very large-scale work lasting around seventy minutes. His last four symphonies make up a quartet of works based on the four seasons.
Raff also composed in most other genres, including concertos, opera, chamber music and works for solo piano.