Steve Evans started a great thread on Atonement analogies over at Times & Seasons. One aspect of the atonement that I have thought quite a bit about that tends to distinguish Mormon approaches to salvation from others is that teaching that salvation is not merely individual, but communal. A few years ago I wrote the following mini-essay focusing on that aspect. Some of my thoughts are similar to greenfrog's comments on the T&S thread.
Mormonism is fairly unique in its emphasis on the communal nature of salvation. We seal husbands and wives to each other, children to parents, the living to the dead (and in past years, living men adopted to other living men). This sealing is the culmination of temple ordinances. In addition, Mormonism emphasizes the concept of Zion: a temporal heavenly community united with the heavenly city.
Mormonism also teaches that “death” is equivalent to “separation”. The “Fall” brought “death” or separation from God; physical death is the separation of spirit and body, etc. The ultimate punishment in the Church is to be separated from the body of the Saints: excommunication.
In Jesus' intercessory prayer in John 17, he prays that his disciples may become one with him and the Father, even as he and the Father are one.
In the temple, men and women are separated until they reach the celestial room. The depiction of the fall of man and his progression through various spheres culminates in a unifying embrace, and that progression and embrace symbolize a (re)unification with Deity.
So, what is it we need to be saved from? Separation, or death, both physical and spiritual. Sin is that which naturally causes separation. Atonement is, quite literally, “at-one-ment”, linguistically, conceptually, and effectively.
The key components of atonement are the willingness of an innocent party to suffer due to the sins of another, forgiveness, and repentance. All these are essential to the concept of atonement. Reconciliation cannot occur if one of the parties is not willing to reach out to the other. The guilty party must repent, and the innocent party must forgive. Sometimes there may be a need for mediation -- and the mediator also provides an important aspect of atonement. Thus, atonement is necessarily a cooperative process. Without repentance, forgiveness is insufficient. Without forgiveness, repentance is likewise insufficient.
Atonement in this sense is by no means unique to Jesus. In fact, he taught that all his followers should drink of the same cup. His life and teachings cannot, in this sense, be separated from atonement. He taught that we should turn the other cheek, walk a mile more than we are compelled, give our cloak as well as our coat when sued, and so forth. He gave examples of forgiveness and mercy and taught that our own judgments would return upon us. (In this light, the teaching that those who do not forgive are guilty of the greater sin makes sense: they are perpetuating and aggravating the existing separation, whereas mercy begets mercy.)
Jesus taught that all of us should become Christs, do his works. When we take upon ourselves his name, we covenant to follow his example.
So, if we are all Christs, what is unique about Jesus? I would suggest that the primary difference is that Jesus is uniquely recognized as the embodiment of God. Thus, we see that God also atones. Without our recognition that God atones for us -- that he is reaching out to us and doing his part to reconcile us again -- we have little motivation to reach out to God. Thus, it is truly through the grace of Christ that we cry, Abba, Father. This is not only a psychological effect; Jesus actually is God atoning for our sins: “the image of the invisible God.”
I agree with Brigham Young's remarks regarding the Deity within us -- we are all part of God and we are all gods. However, for the most part, we do not recognize this. Hence, a visible symbol of God's atonement was sent to provide the ultimate symbol of atonement: “Greater love hath no man than this, that a man lay down his life for his friends.”
Recognition of this helps us to experience pure love, which brings unity and reconciliation. As we experience this, we develop and/or recognize it within ourselves, and we become more forgiving, less judgmental, more Christlike. We then atone for each other until we have a community of Christs who are perfectly one, who are sealed in a great chain and in eternal family units -- Zion, heaven, unification with God, becoming Gods and becoming God.