Belief in reincarnation is a central tenet within the majority of Indian religions, such as Hinduism, Sikhism, and Jainism. In the west, some New Age movements, along with followers of Spiritism also adhere to reincarnation. For the Christian, however, there can be no doubt: reincarnation is unbiblical and must be rejected as false. If reincarnation is true, then there is no Day of Judgment, no need for the Cross and no need to trust in Christ.
Hebrews 9:27 clearly tells us that that we die once and then face judgment. The Bible never mentions people having a second chance at life or coming back as different people or animals. Jesus told the dying criminal on the cross, "Today you will be with me in paradise" not "You will have another chance to live a life on this earth." The Bible teaches that believers go on to eternal life while unbelievers go on to eternal punishment.
People need Jesus because reincarnation does not remove sin. It works with karma, the idea that your past lives of "goodness" or "badness" affects the quality and position of your next incarnation. The purpose of reincarnation is to help you develop perfect karma by which you might achieve a union with the "divine consciousness" after you have learned whatever it is you are supposed to learn.
That might sound good, but it makes no sense. Think about it, if this is true, each person had a first incarnation. That means that each person then had perfect Karma since he had no previous life and had done nothing wrong. So if he had perfect Karma and didn't learn what he was supposed to learn in his first life, what makes him think that after hundreds of incarnations with accumulated bad karma that he will be able to achieve the perfect state of union with the divine consciousness?
And then there's the issue of final authority. When it's time to reincarnate, who or what is the cosmic authority figure that decides whether you've been good or bad? These religions have no God who judges nor a gauge by which we are judged; It's like having a justice system without a judge, it makes no sense.
But what does make sense is that there is one God who has revealed Himself in Jesus Christ and the only way to have our sins forgiven is to trust in Him and not our own efforts through various lives, trying to achieve perfection. That's why you need Jesus, because reincarnation is not only false, it is empty because you just can't win.
Aside from Jesus, no one has ever been perfect. Because of this, no one could ever be good enough to escape the supposed cycle of reincarnation. After death we face judgment, meaning that there is no second chance, that's why you need a Savior. On the day you die you will not go back to the end of the line to try again, you will be judged. Without the righteousness of Christ, you don't stand a chance.