The only way to answer this question is to set a standard definition of the word cult. Google actually gives us two definitions:
1. A system of religious veneration and devotion directed toward a particular figure or object.
2. A relatively small group of people having religious beliefs or practices regarded by others as strange or sinister.
Is the Mormon church a cult? By definition one, yes. By definition two, depends who you ask. You see, by the first definition all of Christianity is a cult, all of Islam is a cult, and pretty much every major world religion is a cult. If all it takes is veneration (worship) and devotion directed toward a particular figure or object, almost everyone in the world belongs to a cult.
Now, almost everyone who hears the word cult uses the second definition. The word cult is inherently negative, and typically means some quirky sect that worships some random, obscure person or object. For example, the cult that followed Haley’s comet believed aliens were in the wake of the comet and would take them to their spaceships if they all drank Kool-aid together. Of course, they all died. When we hear the word cult, this is typically what we think.
The reason people think the Mormon church is a cult is quite simple. The church was founded in 1830 by Joseph Smith. Here is a brief synopsis of its founding:
In 1820, Joseph Smith was 14 years old and very confused by the various religions in the area he lived in upstate New York. He read in James 1:5 that if he lacked wisdom, he could ask of God, who would answer his question. He did just that one morning in a grove of trees near his home. In answer to his prayer, he was visited by God the Father and His Son Jesus Christ. They told him that none of the churches were true and that he would restore the truth to the world.
As part of this, he received many revelations from God and other heavenly messengers. One of these messengers directed him to an ancient record buried in the ground. Smith translated it and we have it today as The Book of Mormon. After translating the book and being taught many things about the gospel of Jesus Christ, Joseph Smith founded the church as The Church of Jesus Christ of Latter-day Saints.
Naturally, Mormons study the life of Joseph Smith and study his teachings. Because of his central role in restoring the gospel, many mistakenly believe that Mormons worship Joseph Smith in some way. This is completely false. Mormons regard Joseph Smith the same way as any prophet, like Abraham, Moses, Isaiah or Peter. Mormons believe there is even a prophet alive today and that he is the President of the church. He is regarded as all of these other prophets, not worshiped by Mormons.
The only figure or object that receives veneration, worship or devotion from Mormons is God the Father and Jesus Christ. This puts Mormons right in line with mainstream Christianity. Now Mormons do have a unique view of the Trinity, but there is nothing quirky or strange about who or what they worship.
Mormons do not worship Joseph Smith. They learn about him the same way Baptists learn about their founder, Methodists learn about their founder, or any religion studies its founder’s teachings. Mormons do believe some things that others might call crazy, but having a quirky religion and being a cult are very different things. Mormons worship the same being as other Christians, meaning they can in no way be considered a cult, only a quirky sect of Christianity.
The Mormon church is not a cult. If you prefer some definition that does indeed consider the Mormon church a cult, then you are calling every world religion a cult.