As i understand it (correct me if I’m wrong) the head of the Mormon church is titled “prophet, seer, and revelator”. I take it that this person then, receives direct revelations from God. Now, without debating what constitutes a “revelation”, what do practicing Mormons do, if they feel the head of the church is wrong? Is it heresy to reject the head prophet’s pronouncements?
A hypothetical case: suppose one day, the head of the church were to issue a statement, upon the lines of:" my dear brothers and sisters. I have come to tell you that much of what you have been taught is wrong. Joseph Smith was not a prophet, and Brigham Young was not a prophet. I have decided that the doctrines of the Anglican Church are true and correct, and i hereby announce my conversion to Anglican Christainity. I urge you to consider the same. that’s all-goodby".
Would you question the head prophet’s word on this? 
Seeing that neither Monty, dangermom, nor any of the boards’ other active Mormons have stepped in yet, I’ll give you as considered an answer as I know how. Disclaimer: IANAM. While I grew up LDS, attended BYU and served a full-time mission, I am not currently Mormon.
The Mormon belief is that a living prophet trumps a dead one. Since God is the source of scripture and revelation, He can certainly give new revelation that supersedes the old - think of the Gospel of Jesus vs. the old Law of Moses - and He does so through his chosen prophet.
However, as a practical question, I don’t think any of the thousands of Mormons I’ve known would follow a prophet who made such an outlandish pronouncement. My guess is that the remaining apostles would declare him insane, fallen or both, and appoint a new prophet.
Now that’s a religion I can get behind, where the prophets are chosen by men, not God.
You were probably being facetious but just in case you weren’t - the apostles are also considered to have been chosen by God. When the prophet dies the Quorum of the 12 Apostles chooses the new one. So if the prophet went obviously off his rocker it seems likely the apostles would fall back on that procedure.
As far as what the average Mormon can do if the prophet makes a statement they disagree with, they may quietly ignore it (much like a Catholic who uses birth control), they can choose to no longer affiliate themselves with the church (my personal choice), or they can publicly express their opinion (which will likely incur some consequence up to and including excommunication).
It doesn’t seem like the LDS situation here would be all that different from the Catholic tradition of a pope proclaiming something ex cathedra, except perhaps in the frequency of such proclamations. Both are going to be tested against traditional belief. If something were to stand in too much contradiction to everything that went before, it’s more likely the LDS body would deny its credibility. As with the mechanism for choosing a pope, the way the individuals are chosen makes it unlikely. Eventually, though, one of these groups is going to pick a geezer that goes nutty from Alzheimer’s and gets goofy in a public situation. In this day of mass communication, that might get interesting.
Until the 10 commandments show up again ex nihilo, all religions are going to rely on some guy being credited for directly channeling the God. Heck, in many mainstream Protestant churches, you’ll hear the Pastor say, “God told me x…” all the time. And many congregations never question it, even if such an admission in my ED would buy him a stay on the Psych ward.
As pendgwen clarified, if such and event took place (i.e. a prophet being removed by the apostles), they would say it was because of revelation given to them by God.
Well, I guess there’s not much for me to add. So I’m off to a BBQ and water balloon fight. Have fun, all. 
Wasn’t there a time when any mormon could claim direct communication with God? It caused so much grief that one day the leader said “Hey you guys, God told me that he only talks to me now.”
Very early on (i.e. during Joseph Smith’s lifetime), numerous other members of the Church claimed to receive revelation from God, and Smith was frequently having to put them in their place. The Doctrine and Covenants and Church history are full of examples of this problem. Smith’s stance (and the Church’s stance from then until now) is that anyone is able to receive revelation for him- or herself, or for those “under” them (family for a father, congregation for a bishop, entire church for the prophet), but those revelations never contradict or supersede revelations from higher-ups in the Church.
For example, a Mormon bishop may receive a revelation that his congregation should hold a bake sale and give the proceeds to the local homeless shelter (i.e. affects only his local congregation, doesn’t contradict current doctrine), but a revelation that his congregation should return to the practice of plural marriage (contrary to current doctrine) would not have come from God.
AFAIUI, current LDS theology is that anyone is entitled to receive revelation relating to their calling (their responsibility). To ensure the revelation is really from God, one is supposed to check it against previously revelations. The Church’s president (who is called that because he is the President of the High Priesthood of the Church) is responsible for a bit more than I am. Gordon B. Hinkley’s calling is to oversee the entire Church. My calling is to assist in overseeing one small quorum of the Aaronic Priesthood and also to assist the Ward Missionary. Obviously, any revelation I would be entitled to receive would not be on a par with that of the President Hinkley’s.
The Church’s practice is to either accept or not accept (we’ll leave out the issue of “rubber stamping” for the moment, if you don’t mind–and even if you do) his claimed revelation. The procedure for accepting it is that the President presents it to the Church during either the annual or semi-annual general conference. Those present will “sustain” or “not sustain” it. Then the membership of the Church throughout the world will do the same at their stake conferences.
Now, what if he were to advance something that would make the membership of the Church say, “Huh? That ain’t right!” Well, another part of our theology is that it just can’t happen. We hold that it’s not in the Lord’s plan to permit the Church’s leader to lead the Church astray.
I’ve been LDS for a long time; however, I have only been active for the last few years. The above is the best of my recollection of the issue. I’ll let other active LDS posters clarify or correct the post and also provide any references from the Scriptures or the General Authorities on this issue.
I just thought of a clarification/correction for my post above. For my calling, my responsibility, I am entitled to the direction of the Holy Spirit for that calling. I would not, as a local ward leader, receive revelation regarding to the governing of the entire church.
Listening to the guidance of the Holy Spirit is another issue and, I think, one for a different thread.
This situation is not really hypothetical – it has happened.
About a hundred years ago, polygamy was an approved policy of the church, based on ‘revelation’ to Joseph Smith/Brigham Young. But the US Congress absolutely refused to admit Utah (or Deseret) as a state as long as they allowed polygamy.
So suddenly, the current prophet had a new ‘revelation’ that said polygamy was no longer acceptable. So the laws of the territory were changed. Then Congress admitted Utah as a state.
But many LDS Church members of the time did not accept this new ‘revelation’. Mostly they split off from the Church, and continued in their own small groups. Even today, there are groups of people who still practice polygamy. I know these groups still consider themselves as ‘Mormon’, but I’m not sure of the exact relationship between them and the official LDS Church.
The relationship is very adversarial. These groups invariably claim that the “main” Mormon Church has fallen into apostasy (usually since about 1890, when polygamy was officially discontinued) and is no longer led by revelation, whereas their own tiny sect (usually 80-200 people, all with the same two or three last names, in a compound of trailer homes somewhere in the 435 area code) is the only “true” LDS Church.
Having lived in Utah for most of the last 15 years, I’ve encountered plenty of these people, in person as well as on the local news. Even as an ex-Mormon, there are not enough :rolleyes: and :mad: to describe how I feel about them.
The Church of Jesus Christ of Latter-Day Saints, for its part, vigorously denounces and disowns these sects, to the point that the prophet or apostles usually reiterate the fact from the pulpit every couple of years.