I think that the problem here is that every denomination has a different definition of what they consider a "Christian" to be.  
 
Mormons define a "Christian" as one who believes in Jesus Christ. This is perhaps the most broad definition.  
 
One of the most restrictive definitions of a "Christian" is someone who believes every part of what is called the Nicene Creed, in which a group of Catholic bishops decided by a compromise on what was the nature of God and Jesus Christ, this includes the definition of the Holy Trinity. 
 
Most all definitions of "Christians" are somewhere between these two extremes. 
 
Mormons do not qualify under the second definition because we disagree with the concept of the trinity as described in the Nicene Creed, but many other faiths reject this definition as well, and they still consider themselves "Christians". I think the best way to answer this question is for Jason to explain exactly what his definition of a "Christian" is, and what a Christian would need to believe in. That way this question can be sorted out in a way that is meaningful to him.

If one wants to be more specific the LDS Church could more accurately be described as New Testament Christians. Those Christian churches that accept the various creeds (Nicene, Athanasian, etc.) could be described as Creedal Christians, etc.

I guess I will give my take on this question. It asks very specifically "How can mormons claim to be Christian"? 
 
First, it seems clear from reading some of the above posts that there is an element of "works" needed for salvation and that Christ has directed all who have been saved to follow these guidelines. As a non-LDS Christian this goes against the gift of salvation from a loving father. If works are still "needed" why did Christ die on the cross? How then is the thief on the cross explained by Mormons? 
 
I have two really good LDS friends who both have said there has to be works needed for salvation because if not "everything would be chaotic" and we all must do good deeds to stay in line. I almost agree except mainstream Christians do good works BECAUSE of salvation not to gain it. Christ was sent to do away with LAW for salvation, man was sinful, heaven is sinless. We needed a perfect savior (again, because man is sinless) to atone for our sins. 
 
I have some VERY good LDS friends who are wonderful people and I trust my family with them. However one commonnality with them is everything is about them. Their lives, what heaven will be like eternity etc... 
I (and how mainstream Christianity is taught) believe we need to get US out of the way as much as possible and put Jesus in our place. Heaven is about HIM, forever, not about us. It is another gift from God. 
 
So to answer the question I don't think Mormons can claim to be Christians, I think they are close. They talk about outer darkness as a place for people who deny God. I believe the Trinity, however if I take Christ out of it and put myself in that place I am afraid I would be doing just that.

There are two terms that need defining first: Salvation and Exaltation Let's define salvation first. Salvation - in the LDS vernacular is to be saved/redeemed from the eternal grip of death and hell through the atonement of Jesus Christ. This is the Grace so prominently mentioned in the New Testament. I think most Christian denominations - even Mormons - can agree on this. But we as Mormons take go a step further. We also believe in Exaltation. In our vernacular we believe that Exaltation is the bestowal of eternal rewards - essentially living with God and his kingdoms in the eternities. Exaltation is based on our knowledge, obedience and essentially our works (or deeds we have done). When Mormons talk Salvation - they talk about the common Christian definition and belief of Salvation. But they also go further and include our concept of Exaltation and include it with the overall topic of Salvation.  
 
I think that's why some Christians and Mormons say they both believe in Salvation, but because both define the word differently - they explain things differently. Mormons do believe in the concept of salvation believed by most Christians, but we stretch that definition to include much more. 
 
I just came across a great newspaper article talking about the difference between Evangelicals and Mormons. Here it is: http://www.deseretnews.com/article/700201923/LDS-Christianity-Differences-that-matter.html 
 
Let me reiterate though. Mormons are Christians based on our definition of the word Christian (a believer and follower of Jesus Christ).

The main difference is that THe lds faith beleives in the Christ fo the Bible. all others believe in the Nicien creed. That is where the trinity was developed. The CHrist of the bible did not lose his body a second time.

In reply to Andrew's "I don't think Mormons can claim to be Christians, I think they are close" I just want to point out (in the nicest way possible) that his logic is basically, "I consider myself a Christian. Mormons have some beliefs that are different than mine. Therefore, Mormons aren't Christians." 
 
Unfortunately, that's not sound reasoning, and the same logic could be used to conclude he's not Christian either (not that I'm saying that he isn't, I'm just suggesting that somebody else in some other denomination could use that same logic and reach the same conclusion about him). 
 
By any common definition of the word 'christian', Mormons most definitely fit the bill. It is only when you start to morph the definition into something narrower and customized that Mormons wouldn't be considered, but then that's true of anything - I could easily invent a definition of 'christian' that excludes Catholics, or one that excludes Protestants, or one that excludes Andrew, but so what? Mormons are Christians, yes. Are they Evangelical Christians? Nope. Are they Nicene Christians? Nope. At the end of the day, *anytime* somebody claims Mormons are not Christians, they are *always* either uninformed about Mormon theology or they are using a contrived, narrow definition of "Christian" which is, intentional or not, disingenuous. "I'm a Christian and I really like chocolate, and I know tons of other Christians who really like chocolate, and I think all true Christians should like chocolate. I have a neighbor who hates chocolate. Therefore, he is not a Christian." It sounds silly, and I mean no insult, but it's precisely the same logic. 
 
Finally, on the whole works vs not question, Mormons most definitely believe that salvation is a gift from God, that without Christ it would be impossible for us to return to live with God, and that we'd be completely lost. However, it's clear that Christ expects something of us in order to receive his gift, he has set conditions we have to meet. So while we can never "earn" salvation or save ourselves, through our inaction or disobedience we can miss out on receiving His gift. So I think I understand why Mormons might appear to you as focusing too much on the individual, I hope you can understand that from our perspective it's more an issue of, "Christ is willing to give me this completely undeserved gift, I'm going to try my best to do what he asked of me so that I can receive it."