What are the differences between 'Mormonism' and Christianity?

Members of the Church of Jesus Christ of Latter-day Saints (commonly called Mormons) consider themselves Christian because they believe in Jesus Christ, follow His teachings, learn of Him and believe that salvation can only come through Christ - and none other. But Mormons do not consider themselves as belonging to the Catholic or Protestant traditions. They believe they belong to the restored church of Jesus Christ - not a remodel of the Catholic Church.

The reasons why many mainstream Christians do not consider 'Mormons' to be Christian are:

Christians believe the Father, Son, and Holy Spirit are one being/essence (the trinity), while 'Mormons' believe that they are three separate beings (the Father and Son having the appearance of man), united in purpose.

Certain more vocal factions among Christians believe that salvation is through grace alone, and that whether or not a person does good deeds on this earth does not matter. 'Mormons' believe that not only does a person need 'belief' in Jesus Christ, but they must strive to become like Him, and follow His example of charity and love. They also believe that one must be baptized by genuine Priesthood authority to be saved.

Christians generally believe that only the Bible is the word of God and that no other book can contain it. 'Mormon' Christians believe that the Bible is the Word of God, and that the Book of Mormon and Doctrine & Covenants are also the Word of God.

Most Christians do not believe that the Mormon Christian belief in building and worshipping in temples is Christian. LDS Christians build temples so that they can offer salvation (through baptisms and other ordinances) for the dead, as described by Paul the apostle. They do not believe that if a man dies without ever hearing of Christ that he will go to hell, but that if his earthly baptism is performed for him in a temple, he will have the opportunity to choose heaven or hell in the afterlife.

Most of Christendom does not believe that God still calls prophets and apostles, as He did in Biblical times, but 'Mormon' Christians believe in modern prophets, apostles, and modern revelation. They believe that God still appears to and speaks to men just as He ever did in the Bible.

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Mormons are Christian, as are Baptists, Lutherans, Catholics, etc.
Each of these churches has its own distinguishing characteristics.
Mormons are actually members of 'The Church of Jesus Christ of Latter-day Saints'.
The Church is named after Christ, whom its members believe is its Head.
LDS members practise Christian ethics and follow the teachings of Christ as do many other Christians around the world.
The prime distinguishing characteristics of the Church are that the Church teaches a Restoration of many vital lost truths over the centuries following the killing off of God's ancient apostles and the Restoration of such lost authority from God to act in God's name on the earth.
In other words, the Church testifies that God has called prophets and apostles today - in these latter days - to teach and guide the church and to prepare for the Lord's Second Coming.
These would be the two most significant differences.
Basically, all Christians should be endeavouring to lead Christlike lives.
This is what 'mormon' Christians also attempt to do.

Answer:

First, while Christians believe that God is spirit (John 4:24), Joseph Smith taught, "God Himself was once as we are now, and is an exalted man, and sits enthroned in yonder heavens." Mormonism also holds to a plurality of gods and contends that "as man is, God once was; as God is, man may become." The Latter Day Saints compromise the nature of the God-man Jesus Christ. In Christianity, Jesus is the self existent creator of all things (Colossians 1:15-20). In Mormonism, he is the spirit brother of Lucifer who was conceived in heaven by a celestial mother and came in flesh as the result of the Father having sex with the Virgin Mary. In sharp distinction to Christian theology, Mormons do not believe that the Bible is the infallible repository for redemptive revelation (2 Timothy 3:16). In their view, the Book of Mormon is "the most correct of any book on earth, and the keystone of our religion." Two further revelations complete the Mormon quad, namely Doctrine and Covenants and The Pearl of Great Price. Doctrine and Covenants is a compilation of divine revelations that includes the doctrine of polygamy. Not until threatened by the Federal government did Mormon President Wilford Woodruff receive a revelation relegating polygamy to the afterlife. The Pearl of Great Price is no less troubling. It was used by Mormons to prevent African Americans from entering the priesthood and from being exalted to godhood. Finally, while Christians believe that they will stand before God dressed in spotless robes of Christ's righteousness (Romans 3:21-22, Philippians 3:9), Mormons contend that they will appear before the heavenly Father dressed in fig leaf aprons holding good works in their hands. According to the Latter Day Saints, virtually everyone qualifies for heaven. Murderers, unrepentant whoremongers, and the world's most vilest people make it into the Telestial heaven. Lukewarm Mormons, religious people, and those who accept the Mormon gospel in the spirit world typically enter the Terrestrial heaven; and temple Mormons make it into the Celestial heaven. Only those who are sealed in secret temple rituals, however, will make it to the third level of the Celestial kingdom and become gods of their own planets.

Another answer:
Mormonism is a subset of Christianity. Protestantism is also a subset of Christianity, as is Catholicism.