Question: How many anti-Christs are named in the Book of Mormon? What happened to them?
Answer: There are three main anti-Christs mentioned in the Book of Mormon.
(1) Sherem was the first one. He confronted Jacob and asked for a sign. He was smitten and fell to the earth. After many days, he told the people he had been deceived by the power of the devil, and he died.
“And now it came to pass after some years had passed away, there came a man among the people of Nephi, whose name was Sherem.
“And it came to pass that he began to preach among the people, and to declare unto them that there should be no Christ. And he did preach many things which were flattering unto the people; and this he did that he might overthrow the doctrine of Christ.” (Jacob 7:1-2)
(2) Nehor was the second one. He was taken by the people before Alma for having slain Gideon by the sword while he was preaching against the church and trying to enforce his priestcraft among the people. He was condemned to die, according to the law, and was taken to the top of the hill Manti. After confessing that what he had taught to the people was contrary to the word of God, he suffered an ignominious (shameful) death.
“And he had gone about among the people preaching to them that which he termed to be the word of God, bearing down against the church;...And he also testified unto the people that all mankind should be saved at the last day.” (Alma 1:3, 4)
(3) Korihor was the third one. He began to preach to the people against the prophecies which had been spoken by the prophets, concerning the coming of Christ. He even denied there was a God. He asked Alma for a sign, and he was struck dumb. He then went from house to house begging for his food and was soon trodden down and killed.
“...and he was Anti-Christ, for he began to preach unto the people against the prophecies which had been spoken by the prophets, concerning the coming of Christ...And ye also say that Christ shall come. But behold, I say that ye do not know that there shall be a Christ...Now Alma said unto him: Will ye deny again that there is a God, and also deny the Christ?..And now what evidence have ye that there is no God, or that Christ cometh not? I say unto you that ye have none, save it be your word only. But, behold, I have all things as a testimony that these things are true...” (Alma 30:6, 26, 39-41)
Source: 400 Questions and Answers About the Book of Mormon by Susan Easton Black, p. 121; The Book of Mormon.