My List of Scripture that Refutes Reincarnation

 Hebrews 9:27
   Just as man is appointed to die once, and after that to face judgment...

This is probably the clearest refutation of reincarnation. Die once, then judgment. There is never any hint of being judged to receive a do-over; it is reward or punishment time.

2 Corinthians 5:10
   For we must all appear before the judgment seat of Christ, so that each one may receive what is due for what he has done in the body, whether good or evil.

Man is judged for what is "done in the body," not a series of bodies.

John 3:3
   Jesus answered him, “Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.”

This reference is clearly a spiritual rebirth, not a corporeal one.  Here on the Bootcamp Planet a person gets only one body, only once. We are here to get our souls saved, not out bodies. Jesus gave us promises about glorified bodies in the age to come, but those are for the future; there is no body reincarnated from your past.

Revelation 20:13
   And the sea gave up the dead who were in it, Death and Hades gave up the dead who were in them, and they were judged, each one of them, according to what they had done.

I underlined 'each one.' In the original, the word is ἕκαστος.  It transliterates in Greek as hekastos
and means individually.

Ezekiel 18:4
    Behold, all souls are mine; the soul of the father as well as the soul of the son is mine...

A clear distinction is made between two separate souls.

Ezekiel 18:20
    The soul who sins shall die. The son shall not suffer for the iniquity of the father, nor the father suffer for the iniquity of the son. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself.

 The entire eighteenth chapter is worth reviewing, but I have pulled only two verses from Ezekiel for this list. God places responsibility upon each individual.

Romans 14:12
    So then each of us will give an account of himself to God.

The idea of individual responsibility is is not compatible with a philosophy of endless chances. At some point, a line has to be drawn and accountability given. The scriptures teach that this line is bodily death.