According to Merriam-Webster, a cult is simply a system of religious beliefs and ritual. In general, a cult is a group that claims to belong to a specific religion but misrepresents any core teaching that would prevent a believer from being saved according to that religion. In Christian terms, a cult is "a religious group that denies one or more of the fundamentals of biblical truth." Specifically, it is a group that claims to be Christian, but whose teaching, if believed, would prevent someone from having a saving relationship with Jesus Christ.
The core of the Christian salvation message is that Jesus Christ is both God and perfect man, that He died and rose again, and that His sacrifice is solely sufficient to pay for our sins and restore our relationship with God. If any group claims to be Christian but deviates from this message, they are a cult. While many Christian sects differ on minor matters, those who teach a different gospel are not Christian. A Christian sect may believe that Christians are obligated to observe the Sabbath; a cult would teach that honoring the Sabbath is a requirement for salvation.
The two most common Christian cult teachings are that Jesus was not God and that salvation is not by faith alone. Both lead to the belief that Jesus' sacrifice was not sufficient to pay for our sins, and our effort is needed in the process of salvation, which is directly contrary to Scripture (Ephesians 2:8-9). The two most prominent churches who teach this are the Mormons and the Jehovah's Witnesses. Mormons teach that Jesus is not God, and that even God had to earn His position as Supreme Being. Jehovah's Witnesses believe Jesus is Michael the archangel. Both cults teach that salvation is the result of faith and those good works which are listed by their respective churches.
Cults are nearly as old as the church, itself. They're particularly dangerous because they may use the same language and claim to be Christian, but their teachings pull people away from God instead of drawing people toward Him. Their words sound right, their adherents are sincere, but their way leads to death (Galatians 1:6-9).
It can be dangerous to only look to dictionaries for such definitions, lot's of dictionaries are biased these days.
Sometimes "Cult" is what the big congregation calls the little congregation, mostly though the church that believes another church is apostate calls it a cult though. Like the catholics calling protostantism a dangerous heresy and the protastants calling the catholic system the largest cult in world history. There can be a lot of nuance but mostly if the people are fanatically closed-minded to the point of almost being braindead... it's a cult.
The specific Christian definition of a cult is �a religious group that denies one or more of the fundamentals of biblical truth.� In simpler terms, a cult is a group that teaches something that will cause a person to remain unsaved if he/she believes it. As distinct from a religion, a cult is a group that claims to be part of the religion, yet denies essential truth(s) of that religion. A Christian cult is a group that denies one or more of the fundamental truths of Christianity, while still claiming to be Christian.
The two most common teachings of cults are that Jesus was not God and that salvation is not by faith alone. A denial of the deity of Christ results in Jesus� death not being a sufficient payment for our sins. A denial of salvation by faith alone results in salvation being achieved by our own works, something the Bible vehemently and consistently denies. The two most well-known examples of cults are the Jehovah's Witnesses and Mormons. Both groups claim to be Christian, yet both deny the deity of Christ and salvation by faith alone. Jehovah's Witnesses and Mormons believe many things that are in agreement with or similar to what the Bible teaches. However, the fact that they deny the deity of Christ and preach a salvation by works qualifies them as a cult. Many Jehovah�s Witnesses, Mormons, and members of other cults are �good people� who genuinely believe they hold the truth. As Christians, our hope and prayer must be that many people involved in the cults will see through the lies and will be drawn to the truth of salvation through faith in Jesus Christ alone.
Groups that fanatically follow a particular leader are cultic in a sense as well. Hank Hanegraaf has explained that there are doctrinal cults (the kind you're pointing out) and sociological cults.
The latter can have the fundamental doctrines in order, but tends to be centered on a particular preacher and be very schismatic. I knew some people who considered that their church and about 3 others around the country were the "right" churches and that probably everyone outside these were unsaved.
One of the doctrinal cults you haven't mentioned is the antinomian cult/doctrinal set that teaches that one can continue in sin after conversion. I've heard this group preach, "A saved man may sin just as much as an unsaved man. The difference is that the saved man feels bad about it."
I'm sure that are other doctrinal cults none of us have mentioned, but that one's pretty prominent in the US lately.
