Punishment

Under the Law of Moses, there were four punishments employed:

compensation,
scourging,
retaliation,
death.  

Compensation

Exodus 22:7-9: If a man shall deliver unto his neighbour money or stuff to keep, and it be stolen out of the man's house; if the thief be found, let him pay double. If the thief be not found, then the master of the house shall be brought unto the judges, to see whether he have put his hand unto his neighbour's goods. For all manner of trespass, whether it be for ox, for ass, for sheep, for raiment, or for any manner of lost thing, which another challengeth to be his, the cause of both parties shall come before the judges; and whom the judges shall condemn, he shall pay double unto his neighbour.

Scourging

Deuteronomy 25:1-3: If there be a controversy between men, and they come unto judgment, that the judges may judge them; then they shall justify the righteous, and condemn the wicked. And it shall be, if the wicked man be worthy to be beaten, that the judge shall cause him to lie down, and to be beaten before his face, according to his fault, by a certain number. Forty stripes he may give him, and not exceed: lest, if he should exceed, and beat him above these with many stripes, then thy brother should seem vile unto thee.

Retaliation

The Lord rarely allowed retaliation, even under the Las of Moses,
but there were exceptions, as shown here:

Exodus 21:22-25: If men strive, and hurt a woman with child, so that her fruit depart from her, and yet no mischief follow: he shall be surely punished, according as the woman's husband will lay upon him; and he shall pay as the judges determine. And if any mischief follow, then thou shalt give life for life, Eye for eye, tooth for tooth, hand for hand, foot for foot, Burning for burning, wound for wound, stripe for stripe.

It must be pointed out in this example that the husband of the offended may ask for a punishment, but it is carried out as the judges, not the requester, determines.

Methods of Death Sentence

STONING:

Leviticus 20:2: ... he shall surely be put to death: the people of the land shall stone him with stones.
Leviticus 20:27: ...shall surely be put to death: they shall stone them with stones: their blood shall be upon them.
Leviticus 24:14: ...and let all the congregation stone him.
Numbers 15:35: ... all the congregation shall stone him with stones without the camp.
Deuteronomy 21:21: And all the men of his city shall stone him with stones, that he die: so shalt thou put evil away from among you; and all Israel shall hear, and fear.

HANGING:

Deuteronomy 21:22-23: And if a man have committed a sin worthy of death, and he be to be put to death, and thou hang him on a tree: His body shall not remain all night upon the tree, but thou shalt in any wise bury him that day; (for he that is hanged is accursed of God;) that thy land be not defiled, which the LORD thy God giveth thee for an inheritance.

Reasons for the Death Penalty under the Law of Moses

Blasphemy

Leviticus 24:14-16: Bring forth him that hath cursed without the camp; and let all that heard him lay their hands upon his head, and let all the congregation stone him. And thou shalt speak unto the children of Israel, saying, Whosoever curseth his God shall bear his sin. And he that blasphemeth the name of the LORD, he shall surely be put to death, and all the congregation shall certainly stone him: as well the stranger, as he that is born in the land, when he blasphemeth the name of the LORD, shall be put to death.... And Moses spake to the children of Israel, that they should bring forth him that had cursed out of the camp, and stone him with stones. And the children of Israel did as the LORD commanded Moses.

False Witness (Testimony)
in some cases

Deuteronomy 19:16-21: If a false witness rise up against any man to testify against him that which is wrong; Then both the men, between whom the controversy is, shall stand before the LORD, before the priests and the judges, which shall be in those days; And the judges shall make diligent inquisition: and, behold, if the witness be a false witness, and hath testified falsely against his brother; Then shall ye do unto him, as he had thought to have done unto his brother: so shalt thou put the evil away from among you. And those which remain shall hear, and fear, and shall henceforth commit no more any such evil among you. And thine eye shall not pity; but life shall go for life, eye for eye, tooth for tooth, hand for hand, foot for foot.

Idolatry

Exodus 22:20: He that sacrificeth unto any god, save unto the LORD only, he shall be utterly destroyed.
Leviticus 20:2-5: Again, thou shalt say to the children of Israel, Whosoever he be of the children of Israel, or of the strangers that sojourn in Israel, that giveth any of his seed unto Molech; he shall surely be put to death: the people of the land shall stone him with stones. And I will set my face against that man, and will cut him off from among his people; because he hath given of his seed unto Molech, to defile my sanctuary, and to profane my holy name. And if the people of the land do any ways hide their eyes from the man, when he giveth of his seed unto Molech, and kill him not: Then I will set my face against that man, and against his family, and will cut him off, and all that go a whoring after him, to commit whoredom with Molech, from among their people.
Deuteronomy 13:6-18: If thy brother, the son of thy mother, or thy son, or thy daughter, or the wife of thy bosom, or thy friend, which is as thine own soul, entice thee secretly, saying, Let us go and serve other gods, which thou hast not known, thou, nor thy fathers; Namely, of the gods of the people which are round about you, nigh unto thee, or far off from thee, from the one end of the earth even unto the other end of the earth; Thou shalt not consent unto him, nor hearken unto him; neither shall thine eye pity him, neither shalt thou spare, neither shalt thou conceal him: But thou shalt surely kill him; thine hand shall be first upon him to put him to death, and afterwards the hand of all the people. And thou shalt stone him with stones, that he die; because he hath sought to thrust thee away from the LORD thy God, which brought thee out of the land of Egypt, from the house of bondage. And all Israel shall hear, and fear, and shall do no more any such wickedness as this is among you. If thou shalt hear say in one of thy cities, which the LORD thy God hath given thee to dwell there, saying, Certain men, the children of Belial, are gone out from among you, and have withdrawn the inhabitants of their city, saying, Let us go and serve other gods, which ye have not known; Then shalt thou enquire, and make search, and ask diligently; and, behold, if it be truth, and the thing certain, that such abomination is wrought among you; Thou shalt surely smite the inhabitants of that city with the edge of the sword, destroying it utterly, and all that is therein, and the cattle thereof, with the edge of the sword. And thou shalt gather all the spoil of it into the midst of the street thereof, and shalt burn with fire the city, and all the spoil thereof every whit, for the LORD thy God: and it shall be an heap for ever; it shall not be built again. And there shall cleave nought of the cursed thing to thine hand: that the LORD may turn from the fierceness of his anger, and shew thee mercy, and have compassion upon thee, and multiply thee, as he hath sworn unto thy fathers; When thou shalt hearken to the voice of the LORD thy God, to keep all his commandments which I command thee this day, to do that which is right in the eyes of the LORD thy God.
Deuteronomy 17:2-7: If there be found among you, within any of thy gates which the LORD thy God giveth thee, man or woman, that hath wrought wickedness in the sight of the LORD thy God, in transgressing his covenant, And hath gone and served other gods, and worshipped them, either the sun, or moon, or any of the host of heaven, which I have not commanded; And it be told thee, and thou hast heard of it, and enquired diligently, and, behold, it be true, and the thing certain, that such abomination is wrought in Israel: Then shalt thou bring forth that man or that woman, which have committed that wicked thing, unto thy gates, even that man or that woman, and shalt stone them with stones, till they die. At the mouth of two witnesses, or three witnesses, shall he that is worthy of death be put to death; but at the mouth of one witness he shall not be put to death. The hands of the witnesses shall be first upon him to put him to death, and afterward the hands of all the people. So thou shalt put the evil away from among you.

Kidnapping

Exodus 21:16: And he that stealeth a man, and selleth him, or if he be found in his hand, he shall surely be put to death.
Deuteronomy 24:7: If a man be found stealing any of his brethren of the children of Israel, and maketh merchandise of him, or selleth him; then that thief shall die; and thou shalt put evil away from among you.

Murder

Exodus 21:12-14: He that smiteth a man, so that he die, shall be surely put to death. And if a man lie not in wait, but God deliver him into his hand; then I will appoint thee a place whither he shall flee. But if a man come presumptuously upon his neighbour, to slay him with guile; thou shalt take him from mine altar, that he may die.
Leviticus 24:17: And he that killeth any man shall surely be put to death.
Numbers 35:30-31: Whoso killeth any person, the murderer shall be put to death by the mouth of witnesses: but one witness shall not testify against any person to cause him to die. Moreover ye shall take no satisfaction for the life of a murderer, which is guilty of death: but he shall be surely put to death.
Deuteronomy 19:11-13: But if any man hate his neighbour, and lie in wait for him, and rise up against him, and smite him mortally that he die, and fleeth into one of these cities: Then the elders of his city shall send and fetch him thence, and deliver him into the hand of the avenger of blood, that he may die. Thine eye shall not pity him, but thou shalt put away the guilt of innocent blood from Israel, that it may go well with thee.

Reviling Parents

Exodus 21:15: And he that smiteth his father, or his mother, shall be surely put to death.
Exodus 21:17: And he that curseth his father, or his mother, shall surely be put to death.
Leviticus 20:9: For every one that curseth his father or his mother shall be surely put to death: he hath cursed his father or his mother; his blood shall be upon him.

Sabbath-Breaking

Exodus 31:14-15: Ye shall keep the sabbath therefore; for it is holy unto you: every one that defileth it shall surely be put to death: for whosoever doeth any work therein, that soul shall be cut off from among his people. Six days may work be done; but in the seventh is the sabbath of rest, holy to the LORD: whosoever doeth any work in the sabbath day, he shall surely be put to death.
Exodus 35:2: Six days shall work be done, but on the seventh day there shall be to you an holy day, a sabbath of rest to the LORD: whosoever doeth work therein shall be put to death.
Numbers 15:32-36: And while the children of Israel were in the wilderness, they found a man that gathered sticks upon the sabbath day. And they that found him gathering sticks brought him unto Moses and Aaron, and unto all the congregation. And they put him in ward, because it was not declared what should be done to him. And the LORD said unto Moses, The man shall be surely put to death: all the congregation shall stone him with stones without the camp. And all the congregation brought him without the camp, and stoned him with stones, and he died; as the LORD commanded Moses.

Sexual Sins

ADULTERY
Leviticus 20:10-12, 14: And the man that committeth adultery with another man's wife, even he that committeth adultery with his neighbour's wife, the adulterer and the adulteress shall surely be put to death. And the man that lieth with his father's wife hath uncovered his father's nakedness: both of them shall surely be put to death; their blood shall be upon them. And if a man lie with his daughter in law, both of them shall surely be put to death: they have wrought confusion; their blood shall be upon them... And if a man take a wife and her mother, it is wickedness: they shall be burnt with fire, both he and they; that there be no wickedness among you.
Deuteronomy 22:22-14: If a man be found lying with a woman married to an husband, then they shall both of them die, both the man that lay with the woman, and the woman: so shalt thou put away evil from Israel. If a damsel that is a virgin be betrothed unto an husband, and a man find her in the city, and lie with her; Then ye shall bring them both out unto the gate of that city, and ye shall stone them with stones that they die; the damsel, because she cried not, being in the city; and the man, because he hath humbled his neighbour's wife: so thou shalt put away evil from among you.

BESTIALITY:
Exodus 22:19: Whosoever lieth with a beast shall surely be put to death.
Leviticus 20:15-16: And if a man lie with a beast, he shall surely be put to death: and ye shall slay the beast. And if a woman approach unto any beast, and lie down thereto, thou shalt kill the woman, and the beast: they shall surely be put to death; their blood shall be upon them.
Deuteronomy 27:21: Cursed be he that lieth with any manner of beast. And all the people shall say, Amen.

FORNICATION:
Leviticus 21:9: And the daughter of any priest, if she profane herself by playing the whore, she profaneth her father: she shall be burnt with fire.

HOMOSEXUALITY:
Leviticus 20:13: If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: they shall surely be put to death; their blood shall be upon them.

RAPE:
Deuteronomy 22:25-29: But if a man find a betrothed damsel in the field, and the man force her, and lie with her: then the man only that lay with her shall die: But unto the damsel thou shalt do nothing; there is in the damsel no sin worthy of death: for as when a man riseth against his neighbour, and slayeth him, even so is this matter: For he found her in the field, and the betrothed damsel cried, and there was none to save her. If a man find a damsel that is a virgin, which is not betrothed, and lay hold on her, and lie with her, and they be found; Then the man that lay with her shall give unto the damsel's father fifty shekels of silver, and she shall be his wife; because he hath humbled her, he may not put her away all his days.
 

Witchcraft
Sorcery
False Prophecy

Exodus 22:18: Thou shalt not suffer a witch to live.
Leviticus 20:6: And the soul that turneth after such as have familiar spirits, and after wizards, to go a whoring after them, I will even set my face against that soul, and will cut him off from among his people.
Leviticus 20:27: A man also or woman that hath a familiar spirit, or that is a wizard, shall surely be put to death: they shall stone them with stones: their blood shall be upon them.
Deuteronomy 13:5: And that prophet, or that dreamer of dreams, shall be put to death; because he hath spoken to turn you away from the LORD your God, which brought you out of the land of Egypt, and redeemed you out of the house of bondage, to thrust thee out of the way which the LORD thy God commanded thee to walk in. So shalt thou put the evil away from the midst of thee.
Deuteronomy 18:20: But the prophet, which shall presume to speak a word in my name, which I have not commanded him to speak, or that shall speak in the name of other gods, even that prophet shall die.