Answer:
Some of the languages of the indigenous peoples of North America had no written form. The indigenous peoples of Australia also had no written language, I believe, in a formal sense. In many cultures have very elaborate art forms that express the elements of a story, but these don't count as formal written languages. Many of these languages have since developed alphabets and written forms. Unfortunately this alone will not prevent many of these now living languages from dying out. Languages are being forever lost every year.
Here are some written languages that do not use an alphabet:
Chinese
Japanese
Cherokee
Ancient Egyptian