With new technology, comes new formats. My initial thought with the Kindle was "I don't want to buy ALL my books from Amazon."
Fortunately, I don't have to.
The Church has many ebooks available for download, but there is not a format labeled "Kindle." Fear not, the Kindle accepts "mobipocket" documents.
The following list can be found at lds.org:
Scripture Study Materials
Standard Works Manuals
Our Heritage
Preparing for Exaltation
Presidents of the Church
Proclamations
The Family
The Living Christ
Gospel Reference
Gospel Principles
True to the Faith
Teaching No Greater Call
Aaronic Priesthood Manuals
Primary Manuals
Music
Church Hymns
Children's Songbook