Gees Joseph Fielding Smith come close to being crazy for some of his outrageous beliefs. Two that come to my mind are how dinosaur bones were from other worlds and were put on earth to test our faith, and he said in 1962 in Hawaii that man would never reach the moon.
Kimball was guilt-ridden and repressed. Crazy? I don't know.
Benson's cold warrior mentality was extreme but at least bordered on defensible in its time (his contemporary fanboys, like Glenn Beck, however, are just trying to pound square pegs into round holes).
Hinckley wasn't crazy. He saw the writing on the wall, if anything.
If you open it up to the whole 20th century, you could include Joseph F. Smith who testified to a congressional committee that he didn't receive revelation from God and that he could not remember the companies for which he was listed as either president or board of directors member.
Kind of depends on how you define crazy. Maybe he was the sane one.
I think Benson was crazy during the 60's and 70's, but just mellow and senile by the time he was president. (Sorry Steve. No offense intended.)
Harold B. Lee may have been pretty crazy. I've wondered if Lee hadn't died after such a short stint as "prophet" what might have happened in the church. I have been told that he was pretty narrow-minded and somewhat of a racist. He may have refused to grant the PH to blacks and maybe kept the church even more backward and insular. The changes under Kimball may not have happened if Lee had lived a long life. That would cause the church to appear even more out of step with the world. Oh well. We will never know.
I can only speak of Presidents I have witnessed during my lifetime: while I was a missionary I saw a General conference talk by ETB sometime in 1987 where he talked about the founding fathers of America appearing to Wilford Woodruff http://lds.org/ensign/1987/11/our-divine-constitution?lang=eng At that point I pretty much assumed he was a loon for espousing such nonsense, and this was one of the final nails in my disbelieving coffin.