I've heard arguments both for the position that Mormons are Christian and for the position that Mormons aren't Christian. I've read the quotes by Hinckley and others that usually get trotted out in such discussions.
The question really only seems relevant to two groups of people: 1) those who believe Christianity is the only true religion so it really matters if one is a ChristianTM or not; and 2) Mormons who don't want to be thought of as "less than" because they are not thought of as part of the Christian majority. The question might also be relevant to anthropologists/socialogists.
To the anthropologist, when considering all of the different religions that have and do exist (Taoism, Buddhism, Hinduism, Paganism, etc), Mormonism clearly is a product of and fits in the camp of Christianity. Mormonism considers the Bible holy scripture and the word of God and features Christ as a god to be worshipped. Clearly, Mormonism has some unique theology and rituals and as such should not be catergorized within the Roman Catholics, or the Protestants, or the Armenians, Coptic Church, or Eastern Orthodox movements.But, Mormonism still fits in the larger umbrella of Christianity nonetheless.
Now, to many Protestants, those differences in theology in Mormonism are all so important. Since Mormonism doesn't fit into their rather overly strict definition of what a Christian must believe, many Protestants don't consider Mormons Christian. But, many people reject the Protestant definition of Christianity as THE definition of Christianity.
Some Mormon leaders, who wanted to emphasize that Mormonism is different/better than the predominant form of Christianity, have said things that one could interpret as them claiming they are not part of what they believe is the corrupt and apostacized Christian movement. But, most, if not all, would claim that they are the true followers of Christ and therefore the true Christians.
Many modern Mormons consider themselves Christian as they look to Christ as their Savior, Lord, and as the Son of God.
Personally, in a lot of ways, I just don't care. I don't believe either Mormonism or Christianity is true (or any other religion). To me, it is like arguing whether the Pharoah Amenhotep's brand of theology (monotheism) can be classified as part of the ancient Egyptian religion which believed in many gods, or not.
I sometimes think we get too caught up in trying to categorize things as opposed to just appreciating the differences and the similarities for what they are.