I was looking for free copies of the LDS scriptures, music, and the children's Book of Mormon Stories. I knew there used to be links in the .mobi format on the old lds.org site, so I went and found them.
- LDS Standard Works, manuals, and music in mobipocket format (Kindle understands this format)
- pdfs of the children's picture scriptures
- You can also take the eReader format and use Calibre to convert it to mobi form
There are now apps in the kindle store for the standard works, hymns, and children's song book, plus lds tools.