Punishment for Fornication (illegal intercourse or adultery) in Islamic law: stoning or flogging.

Iran was in news for sentencing a woman to death by stoning as she was accused of adultery and the punishment was suspended because of objections from Human Rights commission (here). Recently, it emerged that in Sudan each year 40,000 women are flogged for one or other supposedly moral crime (here):

Forty thousand women in Sudan are subject to police whippings for moral transgressions each year, a figure that came to light after a video was circulated on the Internet which showed the public thrashing of a Khartoum woman.

Sudanese feminist and political figure Mariam al-Sadiq al-Madi brought the issue to the attention of authorities, the Sudanese daily al-Sharq al-Awsat reported. The drama of the physical punishments against women in Sudan is much more serious than previously believed," al-Madi said. She said that each year around 600,000 lashes are dealt to women in Sudan.

There was even a case of a Bangladeshi woman dying of flogging (or lashing) she was subjected to (here) on the accusations of adultery. Constitution of Bangladesh is fairly secular but it is not going to stop Muslim moral police to inflict Islamic punishments. What is the proper punishment for adultery according to Islamic laws?
Here, it depends on whether guilty are married or unmarried. If unmarried, then the punishment is flogging in public and for married people it is death by stoning. Now many Muslims say this punishment of stoning to death is not mentioned in Koran. They are right. But Islam is not a Koran only affair; Islam has more to do with what Mohammad did than following Koran.

This is what Koran says on fornication:

(As for) the fornicatress and the fornicator, flog each of them, (giving) a hundred stripes, and let not pity for them detain you in the matter of obedience to Allah, if you believe in Allah and the last day, and let a party of believers witness their chastisement. (24:02, Shakir)

The woman and the man guilty of illegal sexual intercourse, flog each of them with a hundred stripes. Let not pity withhold you in their case, in a punishment prescribed by Allâh, if you believe in Allâh and the Last Day. And let a party of the believers witness their punishment. (This punishment is for unmarried persons guilty of the above crime but if married persons commit it, the punishment is to stone them to death, according to Allâh's Law). (Hilali, 24.02)

In the Hilali's version, the sentence in brackets is his addition and his view. But it is Hadith which carry the weight on this matter. As I said Islam is not Koran only affair, it is because, Koran commands Muslims to follow and obey Mohammad in about 91 verses. A Muslim's faith will not be completed if he believes in only Allah but not Mohammad. Koran even says Mohammad is the perfect example for every Muslim to follow to reach Allah.

He who obeys the Messenger, obeys Allah: But if any turn away, We have not sent thee to watch over their (evil deeds). (YUSUF ALI, 4:80)

The Believers, men and women, are protectors one of another: they enjoin what is just, and forbid what is evil: they observe regular prayers, practise regular charity, and obey Allah and His Messenger. On them will Allah pour His mercy: for Allah is Exalted in power, Wise. (YUSUF ALI, 9:74)

O ye who believe! Obey Allah and His Messenger, and turn not away from him when ye hear (him speak). (YUSUF ALI, 8:20)

Say: "Obey Allah and His Messenger": But if they turn back, Allah loveth not those who reject Faith. (YUSUF ALI, 3:32)

So obey Allah, and obey His Messenger: but if ye turn back, the duty of Our Messenger is but to proclaim (the Message) clearly and openly. (YUSUF ALI, 64:12)

Only those are Believers who have believed in Allah and His Messenger, and have never since doubted, but have striven with their belongings and their persons in the Cause of Allah: Such are the sincere ones. (YUSUF ALI, 49:15)

Ye have indeed in the Messenger of Allah a beautiful pattern (of conduct) for any one whose hope is in Allah and the Final Day, and who engages much in the Praise of Allah. (YUSUF ALI, 33:21)

It is from these verses like these, Islamic scholars and many Muslims conclude that laws in Islam come from Koran and what Mohammad did and say. These traditions of Mohammad exist in Hadith. Though many Hadith were compiled, there are 6 major canonical Hadith in Sunni Islam. Among these 6, two, by Bukhari and Muslims, are considered as Sahih meaning authentic or verified. It is in this Hadith, one will find that Mohammad did prescribe stoning for adultery.

'Umar said, "I am afraid that after a long time has passed, people may say, "We do not find the Verses of the Rajam (stoning to death) in the Holy Book," and consequently they may go astray by leaving an obligation that Allah has revealed. Lo! I confirm that the penalty of Rajam be inflicted on him who commits illegal sexual intercourse, if he is already married and the crime is proved by witnesses or pregnancy or confession." Sufyan added, "I have memorized this narration in this way." 'Umar added, "Surely Allah's Apostle carried out the penalty of Rajam, and so did we after him." (Sahih Bukhari; 8, 82, 816).

A man from among the people, came to Allah's Apostle while Allah's Apostle was sitting in the mosque, and addressed him, saying, "O Allah's Apostle! I have committed an illegal sexual intercourse." The Prophet turned his face away from him. The man came to that side to which the Prophet had turned his face, and said, "O Allah's Apostle! I have committed an illegal intercourse." The Prophet turned his face to the other side, and the man came to that side, and when he confessed four times, the Prophet called him and said, "Are you mad?" He said, "No, O Allah's Apostle!" The Prophet said, "Are you married?" He said, "Yes, O Allah's Apostle." The Prophet said (to the people), "Take him away and stone him to death." Ibn Shihab added, "I was told by one who heard Jabir, that Jabir said, 'I was among those who stoned the man, and we stoned him at the Musalla ('Id praying Place), and when the stones troubled him, he jumped quickly and ran away, but we overtook him at Al-Harra and stoned him to death (there).' " (Sahih Bukhari, 8; 82, 814)

I heard the Prophet ordering that an unmarried person guilty of illegal sexual intercourse be flogged one-hundred stripes and be exiled for one year. Umar bin Al-Khattab also exiled such a person, and this tradition is still valid. (Sahih Bukhari; 8, 82, 818)

I asked 'Abdullah bin Abi 'Aufa about the Rajam (stoning somebody to death for committing illegal sexual intercourse). He replied, "The Prophet carried out the penalty of Rajam," I asked, "Was that before or after the revelation of Surat-an-Nur?" He replied, "I do not know." (Sahih Bukhari; 8, 82, 824)

.........I do not know; perhaps it portends my death, so whoever understands and remembers it, must narrate it to the others wherever his mount takes him, but if somebody is afraid that he does not understand it, then it is unlawful for him to tell lies about me. Allah sent Muhammad with the Truth and revealed the Holy Book to him, and among what Allah revealed, was the Verse of the Rajam (the stoning of married person (male & female) who commits illegal sexual intercourse, and we did recite this Verse and understood and memorized it. Allah's Apostle did carry out the punishment of stoning and so did we after him.                                         I am afraid that after a long time has passed, somebody will say, 'By Allah, we do not find the Verse of the Rajam in Allah's Book,' and thus they will go astray by leaving an obligation which Allah has revealed. And the punishment of the Rajam is to be inflicted to any married person (male & female), who commits illegal sexual intercourse, if the required evidence is available or there is conception or confession.......... (Sahih Bukhari, 8, 82, 817)

Finally from the manual of sharia law of Shafi'i school of Sunnu Islam, Reliance of Traveller, (Division 'o', Chapter 12):

*2*Chapter O12.0: The Penalty for Fornication or Sodomy
@O12.1
The legal penalty is obligatorily imposed upon anyone who fornicates or commits sodomy (A: provided it is legally established (def: n11.2 (O:) ) ) when they:
(a) have reached puberty;
(b) are sane;
(c) and commit the act voluntarily;
no matter whether the person is a Muslim, non-Muslim subject of the Islamic state, or someone who has left Islam.
@O12.2
If the offender is someone with the capacity to remain chaste, then he or she is stoned to death (def: o12.6), someone with the capacity to remain chaste meaning anyone who has had sexual intercourse (A: at least once) with their spouse in a valid marriage, and is free, of age, and sane. A person is not considered to have the capacity to remain chaste if he or she has only had intercourse in a marriage that is invalid, or is prepubescent at the time of material intercourse, or is someone insane at the time of marital intercourse who subsequently regains their sanity prior to committing adultery.
If the offender is not someone with the capacity to remain chaste, then the penalty consists of being scourged (def: o12.5) one hundred stripes and banished to a distance of at least 81 km./50 mi. for one year.
@O12.4
Someone who commits fornication is not punished if he says that he did not know it was unlawful, provided he is a new Muslim or grew up in a remote (O: from Islamic scholars) wilderness, though if neither of these is the case, such a person is punished.
@O12.5
An offender is not scourged in intense heat or bitter cold, or when he is ill and recovery is expected (until he recovers), or in a mosque, or when the offender is a woman who is pregnant, until she gives birth and has recovered from childbed pains. The whip used should be neither new nor old and worn-out, but something in between. The offender is not stretched out when scourged, or bound (O: as his hands are left loose to fend off blows), or undressed (O: but rather an ankle-length shirt is left upon him or her), and the scourger does not lay the stripes on hard (O: by raising his arm, such that he draws blood).  The scourger distributes the blows over various parts of the body, avoiding the vital points and the face. A man is scourged standing; a woman, sitting and covered (O: by a garment wrapped around her).  If the offender is emaciated, or sick from an illness not expected to improve, then he or she is scourged with a single date palm frond (O: upon which there are a hundred strips, or fifty. If a hundred, such an offender is struck once with it, and if fifty, then twice), or with the edge of a garment.
@O12.6
If the penalty is stoning, the offender is stoned even in severe heat or cold, and even if he has an illness from which he is expected to recover. A pregnant woman is not stoned until she gives birth and the child can suffice with the milk of another.