The concept of reincarnation is completely without foundation in the Bible, which clearly tells us that we die once and then face judgment (Hebrews 9:27). The Bible never mentions people having a second chance at life or coming back as different people or animals. Jesus told the criminal on the cross, 'Today you will be with me in paradise" (Luke 23:43), not "You will have another chance to live a life on this earth." Matthew 25:46 specifically tells us that believers go on to eternal life while unbelievers go onto eternal punishment. Reincarnation has been a popular belief for thousands of years, but it has never been accepted by Christians or followers of Judaism because it is contradictory to Scripture. http://www.gotquestions.org/reincarnation.html
In some religions you are. I can think of Hindiusm and Buddhism off the top of my head. Also some sects of my religion (Kemetic/ancient Egyptian) believe in it. So it depends what religion you believe in.
You are referring to reincarnation. Reincarnation is a myth, an idea entirely foreign to that has been revealed by God. In Hebrews 9:27, Bible teaches that it is appointed to man to die once, and then face judgement. Even the Catechism is against reincarnation (CCC 1013). Ultimately, we will go to heaven, and be with God forever, or go to hell, which is eternal exile from God's loving presence. Of course, on the way to heaven, a person may need purification in purgatory. Reincarnation denies the need for a Savior. Titus 3:5 says that we are not saved by works of righteousness, but by the renewal offered by the Holy Spirit. Reincarnation is a philosophy that says we have to continually "work" to improve ourselves, allowing us to come back to life as something better than before. According to this philosophy, the death of Christ for our sins has no meaning because our salvation is totally dependent on our continued work. (My answer continues in the comments)