According to Mayo Clinic, the point at which a fever becomes dangerous depends upon age and other accompanying symptoms. It is generally advised to seek treatment if the fever rises above 102 degrees Fahrenheit in adults and children over 3 months old.
HealthyChildren.org explains that, contrary to common opinion, it takes a fever as high as 108 degrees to cause brain damage. While the fever itself is not dangerous, Mayo Clinic explains that fevers lasting longer than three days or higher than 102 in adults can signify serious underlying conditions. Fevers accompanied by headache, confusion and abdominal pain require emergency medical treatment.