We read in the Book of Mormon and the Bible that Christ appeared to His servants throughout history. Is there any evidence that all Prophets of the Church have seen Him in person?
We have no way of knowing for certain, because it is not usually announced publicly when such a sacred event occurs. I have no issue with thinking that it is possible. I even think it could be quite likely. Especially given a quote from Oliver Cowdery to the Quorum of the Twelve Apostles that was kindly provided to me in research for this answer:
You have been indebted to other men in the first instance for evidence; on that you have acted; but it is necessary that you receive a testimony from Heaven for yourselves; so that you can bear testimony to the truth of the Book of Mormon, and that you have seen the face of God. That is more than the testimony of an angel. When the proper time arrives, you shall be able to bear this testimony to the world. When you bear testimony that you have seen God, this testimony God will never suffer to fall, but will bear you out; although many will not give heed, yet others will. You will, therefore, see the necessity of getting this testimony from Heaven.
“‘Never cease striving till you have seen God face to face. Strengthen your faith; cast off your doubts, your sins, and all your unbelief, and nothing can prevent you from coming to God. Your ordination is not full and complete till God has laid His hands upon you. We require as much to qualify us as did those who have gone before us; God is the same. If the Saviour in former days laid his hands on his disciples, why not in latter days?
In this example we see that it could be a mandatory part of becoming an Apostle. Once again, it would be a very sacred event, hence the reason we don’t hear about it when it occurs.
A related, and interesting thing to note, though, is that each of us has the opportunity to be visited by the Lord as we prove ourselves prepared for such an event. There is another event that is not discussed too often in the Church called ‘receiving the Second Comforter’. In short, when we reach such a point of righteousness, the Savior Jesus Christ himself will appear to us. The Bible Dictionary says this on the matter;
Two Comforters are spoken of. The first is the Holy Ghost (John 14:16–27; Moro. 8:26; D&C 21:9; 42:17; 90:11). The Second Comforter is the Lord Jesus Christ Himself. “When any man obtains this last Comforter, he will have the personage of Jesus Christ to attend him, or appear unto him from time to time, and even He will manifest the Father unto him” (D&C 88:3–4; 130:3; HC 3:381). See also Holy Ghost.
Surely we don’t think that the privilege of seeing our Savior for ourselves would be restricted to the Prophets. All the blessings of righteous obedience to the Gospel of Jesus Christ are available to each and every one of us. Clearly this includes the visitation of Christ himself.
Now, I must remind you that such an event would clearly be a very sacred one, thus very unlikely to be discussed publicly. There are records of the then current Prophets of the Church seeing the Savior from time to time, but they are desperately rare. Should such events be made public simply because they have happened? I don’t think so. There are special and personal events that have taken place between my wife and me in public places, and with other family. Even those that are not spiritual in nature are events that I keep to myself because of the precious nature of them. They are dear to my heart and to tell them to the world lessens their value to me. Were I granted such an opportunity to see my Savior, I would hardly think to tell anyone outside my home, much less the world at large.
Having said that, an important question related to yours would be this; why would we need to know if Christ has appeared to all the Prophets since Joseph Smith’s first vision?
I can see the appeal of it, but the spiritual benefit of such knowledge is more difficult for me to grasp. For example, I have a firm testimony of Joseph Smith’s first vision. I also have a firm testimony that each and every prophet to follow Joseph Smith has been called of God to that position. I have a firm testimony that the revelations given to the Prophets have been, and continue to be the will of God given to us, to strengthen us and guide us back to His presence at the last day.
It surely would be wonderful to have accounts written that Christ still appears to his Prophets today, and as I said above, it wouldn’t surprise me at all if He does. At the same time, my faith in Christ, and my belief in His word does not require me to know whether or not He still does so.