Are there any denominations in Christianity that believe that one can get to heaven without actually being a Christian?
Catholics believe this, in fact recently the Pope said atheists can get into Heaven
Seventh Day Adventists believe that non Christians can get into Heaven
The Church of Jesus Christ of Latter-day Saints, (LDS Church) or Mormonism, teaches that those who die without knowledge of LDS theology will have the opportunity to receive a knowledge of the gospel of Jesus Christ in the spirit world.
Early Christians were divided on this.
Justin Martyr (c. 100-c. 165) said, "Those who lived according to reason [the logos] are Christians," even though they did not know about Jesus.
Tertullian (c. 160-c. 220) claimed that it had been a common belief since the days of the apostles that Jesus descended to hell and preached the gospel. There was debate, though, as to who benefited from the preaching.
Irenaeus (c. 130-c. 200) and Tertullian held that Jesus delivered only the believers of the Old Testament from hell. On the other hand, Clement of Alexandria (mid-100s), Origen (c. 185-c. 254), and Athanasius (c. 296-373) taught that Jesus delivered from hell both Jews and Gentiles who accepted the gospel and that postmortem evangelism continues even today.
Augustine (354-430) rejected such ideas, arguing that before we die we must know about Jesus in order to be saved. Consequently, he believed that all the unevangelized are condemned to hell. Much later, Thomas Aquinas (c. 1225-74) agreed with Augustine on the necessity of knowing about Jesus, but went further to claim that for those few "brought up in the forest or among wolves," God would send the gospel message through miraculous means.
I also found these books in my research on the answer to this question:
ADDENDUM: In response to Caleb's comments I am adding the following quotation from the Cathechism of the Catholic church in support of its official teachings.
VI. THE NECESSITY OF BAPTISM
1257 The Lord himself affirms that Baptism is necessary for salvation.60 He also commands his disciples to proclaim the Gospel to all nations and to baptize them.61 Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament.62 The Church does not know of any means other than Baptism that assures entry into eternal beatitude; this is why she takes care not to neglect the mission she has received from the Lord to see that all who can be baptized are "reborn of water and the Spirit." God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.
1258 The Church has always held the firm conviction that those who suffer death for the sake of the faith without having received Baptism are baptized by their death for and with Christ. This Baptism of blood, like the desire for Baptism, brings about the fruits of Baptism without being a sacrament.
1259 For catechumens who die before their Baptism, their explicit desire to receive it, together with repentance for their sins, and charity, assures them the salvation that they were not able to receive through the sacrament.
1260 "Since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partakers, in a way known to God, of the Paschal mystery."63 Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.
1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them,"64 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.