A useful summary from the [1] New York Times, with thanks to Nicolei and RB. The sources are Amnesty International and the U.S. State Department.

Islamic law based on the Koran is applied in broadly different ways across the Islamic world. A sampling:

Religious States or Regions Within States

IRAN

Legal Codes

Stoning to death is prescribed for offenses (including adultery and
prostitution). The penal code includes these specifications: "The stones should not be too large so that the person dies on being hit by one or two of them; they should not be so small either that they could not be defined as stones."

Regulations updated in 2003 specify that flogging is to be carried out with leather cords 1.5 cm. thick and 1 meter long.

Enforcement: How It Works

Sentences of death by stoning may include a prison term first, or lashings, or both. A moratorium on stoning was issued in 2002, but sentences continued to be handed out.

Recent Cases

2001: Two women were known to have been stoned to death, including one after serving eight years in prison who was convicted of adultery and "corruption on earth."

This is a Qur'anic term: "And We decreed for the Children of Israel in the Scripture: Ye verily will work corruption in the earth twice, and ye will become great tyrants" (17:4).

Two others were reportedly sentenced to death by stoning; it is not known if the sentences were carried out. At least 285 people were flogged, many in public.

2002: At least three were reported sentenced to death by stoning. Amnesty International recorded 9 amputations as punishments, including one cross amputation (for example, a right hand and left foot)....

That too is based on the Qur'an: "The punishment of those who wage war against Allah and His Messenger, and strive with might and main for mischief through the land is: execution, or crucifixion, or the cutting off of hands and feet from opposite sides, or exile from the land: that is their disgrace in this world, and a heavy punishment is theirs in the Hereafter" (5:33).

2004: An Iranian newspaper reported the sentencing of a man to 80 lashes and 10 years imprisonment, to be followed by execution by stoning for running a brothel. Another man was flogged with 80 lashes and died 4 days later after conviction on charges including possession of a medicine containing alcohol, consuming alcohol in the early 1980's, possession of a satellite dish and aiding his sister's "corruption" in having boyfriends.

NIGERIA

Legal Codes

The 1959 code allowed for limited Shariah law in northern Muslim areas but prohibited sentences of stoning and amputation. After civilian rule resumed in 1999, 12 states adopted new Shariah codes, resuming those punishments.

How It Works

The new codes added specific punishments: for theft, amputation of the hand; for drinking alcohol, flogging; for adultery, death by stoning.

Recent Cases

2001: Bariya Ibrahima Magazu, a street hawker believed to be 17 or younger, received 100 lashes in January at the Higher Shariah Court in Tsafe in front of dozens of her neighbors. She had been sentenced to 100 lashes for having sexual relations outside marriage and 80 lashes for falsely accusing three men of coercing her into having sex.

The accusation was probably declared false when the men denied it. In Sharia courts in such cases, the woman's testimony is inadmissible, but the man's is taken at face value (cf. 'Umdat al-Salik o24.9).

Read it all. There is a great amount of important information here.