What's the difference between resurrection and reincarnation?

Several different religions have various teachings on reincarnation, including Hinduism, Jainism, Sikhism, and Taoism, among others. Their teachings differ slightly, but all of them are in opposition to the tenets of the Christian resurrection. Here are some of the similarities and differences.

In reincarnation, an individual dies and comes back to life again in a different body to live on earth again. This reincarnated (which means “returning to flesh again”) person has no knowledge of the past life. In resurrection, the person rises from death with a new body, but with full consciousness of the past. In Revelation 6:10 we learn of martyrs asking God when their deaths will be avenged, showing that they remember the past.

In reincarnation, people’s good deeds usually influence a favorable next life while bad deeds an unfavorable next life. In resurrection, both good and evil are raised to life to stand before God for judgment. Judgment will depend on two deciding factors. If one has rejected God in life, then eternal damnation. If one has accepted Jesus, then rewards will be given or not depending on the faithfulness of one’s works.

Revelation 20:11-15 portrays the Great White Throne judgment, where people are dealt with according to their names in the Book of Life, or according to their works. Several passages in the gospels teach us about how God will judge us and give us rewards.

The cycle of reincarnation continues multiple times. But resurrection happens once (with few exceptions, such as Jesus raising someone from the dead earlier). Hebrews 9:27 tells us that after we die once, then comes the judgment. Reincarnation is wholly impersonal; no God looks over the process. You can have no guarantee how many good deeds you’ve done will break the cycle and bring you further along, or even if there is a more favorable “further along.” You have little help in making a bad life better. But when we receive Christ and repent of our sins, God gives us the indwelling Holy Spirit to help us live righteous lives and prepare us for a favorable judgment. Hebrews 13:5 tells us that he who created us will never leave nor forsake us.

Reincarnation is full of unknowns. You don’t know how many bad deeds were committed in the past life, nor do you know what the standard is for good and bad deeds. But in Christianity, God has placed all our blame upon his Son Jesus Christ and punished him in our place on the cross. We may simply confess and get right with God, and know that all our past sins will be washed away. We may knowingly arrive at the throne of Jesus with our sins forgiven. We know the standards of right and wrong because God’s Bible guides us.

In addition to David Stratton's great answer, reincarnation has a very different idea of the nature of the soul and spirit. As you can see in the word's form, it is based on incarnation, when a spirit takes on flesh. The Eastern religions which believe in reincarnation believe that the soul or spirit is eternal and just temporarily takes on a body.

This is very different from the Judeo-Christian view of humanity which says that the souls/spirits of people did not exist before they were created by God, and that the essence of a person is a soul and spirit being with a body. Those who believe in resurrection believe that when a person dies and their soul/spirit is separated from their body it is a temporary state, and that resurrection will return them to their proper embodied state, in which they will remain for ever after.

Reincarnation involves living again, but having another life in a new body, as a new person/being.

On this one, Wikipedia is as good a source as any.

Reincarnation is the religious or philosophical concept that the soul or spirit, after biological death, begins a new life in a new body that may be human, animal or spiritual depending on the moral quality of the previous life's actions. This doctrine is a central tenet of the Indian religions.1 It is also a common belief of various ancient and modern religions such as Spiritism, Theosophy, and Eckankar and is found in many tribal societies around the world, in places such as Siberia, West Africa, North America, and Australia.2

Resurrection involves living again in your own body (or perhaps a glorified version of it), as yourself.

And again with the Wikipedia definition.

Resurrection (anglicized from Latin resurrectio) is the concept of a living being coming back to life after death. It is distinguished from resuscitation (see below), and is a religious concept used in two distinct respects: a belief in the resurrection of individual souls that is current and ongoing (Christian idealism, realized eschatology), or else a belief in a singular "Resurrection of the Dead" event at the end of the world. The Resurrection of the Dead is a standard eschatological belief in the Abrahamic religions. In a number of ancient religions, a life-death-rebirth deity is a deity which dies and resurrects. The death and resurrection of Jesus is the central focus of Christianity.