The Short Version
This is one of history's most persistent myths. No horned Viking helmet has ever been found in any archaeological dig. The only preserved Viking Age helmets — the Gjermundbu helmet (~875 AD) and the Yarm helmet — are both horn-free. The famous horned helmets (Viksø) are Bronze Age ceremonial artifacts from ~900 BCE, predating Vikings by roughly 1,800 years. The modern stereotype was popularized by costume designer Carl Emil Doepler for Wagner's 1876 opera cycle.