One of these is that Joseph Smith (or Brigham Young or Bruce R McConkie) said that if a man has been home from his mission a year (or turns 25 or turns 27) he is a menace to society.
Another is that Joseph Smith said that the constitution would one day hang by a thread, and that someone from Zion would ride in on a White Horse and save it.
This "White Horse Prophesy" has been getting some media attention lately, especially from Idaho, because a candidate for Governor there has been hosting meetings where he only wants LDS Priesthood holders attending so he can discuss this prophecy. Well, that has led the church to issue the following statement:
"The Church of Jesus Christ of Latter-day Saints is politically neutral and does not endorse or promote any candidate, party or platform. Accordingly, we hope that the campaign practices of political candidates would not suggest that their candidacy is supported by or connected to the church.
"The so-called 'White Horse Prophecy' is based on accounts that have not been substantiated by historical research and is not embraced as Church doctrine."