What is the farthest back an LDS Member has traced his family tree? Knowing how important genealogy research is to LDS leads me to wonder how far back any of us could trace our family tree. Have any LDS members been able to trace back to any biblical characters?
Robert C. Gunderson, Senior Royalty Research Specialist, of the Church Genealogical Department stated, in regards to the possibility of accurately tracing back to Adam and Eve, that the answer is No.  The reason being that European royal genealogy before 500s A.D. Cannot be verified.  This would exclude biblical characters as well.

See
https://familysearch.org/blog/en/family-tree-adam-eve/

https://familysearch.org/blog/en/family-tree-adam-eve-part-2/

It's probably not possible/easy to know who has traced the furthest back since there are so many people doing it and their records aren't all public.