According to The Guardian:
Peter K Austin has published 11 books on minority and endangered languages, including 12 Australian Aboriginal languages, and holds the Märit Rausing Chair in field linguistics at the School of Oriental and African Studies where he is also director of the Endangered Languages Academic Programme. His most recent book is 1000 Languages: The Worldwide History of Living and Lost Tongues, which explores the state of languages around the world.
Austin's top 10 endangered languages are:
Here's the full article, Top 10 Endangered Languages.
Let us know what you think and if you know of any other languages on the verge of being endangered in the comments.