In Mormonism, members of the Church of Jesus Christ of Latter-day Saints strongly believe in the Atonement of Christ.
The Atonement of Christ started in the pre-earth life, when both Jesus and Lucifer offered to be the savior. Lucifer wanted power, and did not care about the plan. Jesus loved the people and did not want power like Lucifer. God chose Jesus instead of Lucifer, which on a side note caused Lucifer to lead a third of the Lord's children away from Him.
Later, after Jesus was born and raised, he preached to the people, established and ordained disciples, and later on, while Judas Iscariot went to the Priests to betray Him, Jesus went to the Garden of Gethsemane, and went through excruciating pain, bleeding out of every pore, and feeling every sin that was ever committed. He did not want to do this, saying to the Lord, "O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt." He loved us, and he atoned for everyone's sins. He sealed this and the prophecies of the prophets by dying on the cross. He was able to overcome physical death and spiritual death, and allowed everyone a chance to come back to him and Heavenly Father, our God.