This depends on the definition of Christian. It also depends on your definition of Mormon.
For "Mormon", I will take this word to mean a member of the Church of Jesus Christ of Latter Day Saints (LDS), the largest and most missionary-oriented Mormon denomination in the world.
If by "Christian" we mean someone who calls them self a Christian, then Mormons are definitely Christians, as they do consider themselves to be. This definition is generally the one used when statistics are provided, such as "There are 2 billion Christians in the world".
However, if by "Christian" we mean someone who follows the Biblical model given to us by Jesus Christ, then Mormons are most definitely NOT Christian.
The differences between Mormons and Biblical Christians are so numerous that I will not even attempt to make a comprehensive list, but I will state a few. The list of conflicts below is arranged in what I personally consider to be the order of doctrinal importance. The last two have no real doctrinal significance, but I find them uniquely interesting.
1. Christians claim that there is only one God (Deuteronomy 4:35; Deuteronomy 32:39; 1 Samuel 2:2; 2 Samuel 7:22; Isaiah 46:9), that He is God eternally (Psalm 90:2; Revelation 22:13; Malachi 3:6; Genesis 1:1; John 1:1; Psalm 93:2), that He has never been human (Malachi 3:6; Numbers 23:19), that nothing will ever be comparable to Him (Lamentations 5:19; Psalm 90:2; Job 38), and that humans will always be human, even in the afterlife (Revelation 21:3). Mormon prophet Lorenzo Snow, the fifth LDS President, declared in 1840, "As man is, God once was; as God is, man may become." (In hearing this, many Christians are reminded of Genesis 3:5)
2. Christians believe that only those with faith in the one true God who sent His only Son, Jesus Christ, will go to heaven (John 3:18; John 14:6; Hebrews 11:6; John 6:44; John 6:53-54; Romans 10:9-10). Mormons believe that everyone will go to heaven (D&C 76:96-103), except the most heinous of criminals, known as Sons of Perdition (D&C 76:28-39).
3. Christians believe that the path to eternal fellowship with God the Father is through the finished work of Jesus Christ (John 14:6; Matthew 5:17; John 19:30). Mormons believe that the path to "heaven" has been secured by the finished work of Jesus Christ, but for fellowship with the Father, each person must rely on his or her own personal works and deeds (Galatians 2:16; Romans 3-4; Romans 9; Romans 11:6; Ephesians 2:9; 2 Timothy 1:9).
4. Christians take the Old and New Testaments of the Bible to be doctrinally authoritative. Mormons accept much of the Bible, but also rely heavily on the Book of Mormon, the Doctrines and Covenants, and the Pearl of Great Price -- three other books that often conflict with Biblical teachings. Where these three conflict with Biblical teachings, the Bible is not considered doctrinally authoritative, but rather is rejected as incorrectly copied or incorrectly translated.
5. Christians have good reason to not consider Joseph Smith to have been a prophet of God, but rather to have been a heretical blasphemer, due to his rejection of Biblical authority and his failed prophecies (Deuteronomy 18:21-22; Matthew 7:15), such as his 1832 prophecy regarding the Mormon Temple in Zion, Missouri, which was to be built within his generation and has still not been built by the LDS church to this day (D&C 84:3-5). Mormons consider Joseph Smith to have been a prophet of God.
6. Christians have no inherent reason (no reason that flows directly from being a Christian) to assume that Native Americans are descended from the Biblical Hebrews. Mormons believe that at least some Native American tribes are directly descended from Joseph (Jacob 1:14; D&C 54:8; D&C 28:8-9,14; D&C 30:6; D&C 32:2). The Mormon prophet Joseph Smith seems to have asserted that all Native Americans originally came from the Hebrew people. Modern-day Mormons generally do not agree with that position.
7. Christians have no inherent reason (no reason that flows directly from being a Christian) to assert that the Apostle John did not die approximately two thousand years ago. Mormons believe that the Apostle John has never died and continues to roam the earth. (John 21:23)