There is a division of thought on the matter.
Even Moslems are divided. Many of them still believe in pre-Koranic religious standards, and for them he comes back as someone else.
Well, so much for reincarnation theories.
The only one everybody seems to agree on is that he will be judged on the Day of Judgment at the End of Time.
Jews have their own Covenant with God and He will know what to do when the time arrives.
LOL, uh, no. The idea is that the soul is not the physical body. Reincarnation is not possession. It's the matching of a body with the development of the soul, so as to support the continued approach to God. It is not the takeover of another living being.
Reincarnation also does not avoid Judgement - in fact, the Judgement is what determines the next body/life, up to and including hell, or heaven. Reincarnation also neatly explains why people are born into such tremendously different situations, yet all are subject to the same divine law (meaning obeying that law seems much easier to some than others).
In fact, about the only seriously blocked common Christian theological teaching reincarnation refutes is a permanent hell (since the karma, or balance of good and evil actions, that sends someone to hell will eventually be exhausted). Because to declare hell permanent, means that it is possible for hate to defeat God's love, or for someone to actually experience God and yet not turn away from evil, or for God to give up on someone as hopeless.
Obviously, each of these issues have it's proponants, sceptics, and dismissers.
Well, so much for reincarnation theories.
Actually, reincarnation means we get to discuss theory over and over again until we get it right : )
Buddhists certianly to not believe in a judgment day at the end of time. I don't think Hindus do either.