Reincarnation
For a Christian there can be no possibility of belief in reincarnation. The letter to the Hebrews tells us, "it is appointed to man to die once and then the judgment" (Heb 9:27). The Church has always taught that our life here on earth is a probation for which we will be judged against the laws of God and the teachings of Christ and thereby our eternal destiny determined (cf. Mt.13 & 25 on the judgement, and separation of good from evil.)
The popularity of reincarnation is therefore easy to understand. It liberates one from acknowledging a revealed moral law and, in fact, most new agers have a very eclectic moral code that amounts to total self-judgment about what is good or evil. How liberating to know that if one doesn't achieve "perfection," there's another go-around in which to make the attempt. Or how depressing! In any case, it is simply not the truth, and an obstacle to the real salvation and perfection offered through Jesus Christ.