Apostasy is still punishable by death in many countries. Because Islam and the state are so closely related, leaving the Islamic faith can still be thought of by some as an act of political betrayal, especially in today's climate of polarization between Muslim and (Judeo-Christian) Western societies. Charges of apostasy are also often used against political enemies and intellectuals who make controversial claims about Islam or challenges conventional social standards.
Currently, the following countries have laws sanctioning the death penalty as a punishment for apostasy: Afghanistan, Iran, Mauritania, Pakistan, Qatar, Saudi Arabia, Sudan, and Yemen.
Even in countries where the death penalty is not legally enforceable, there may be other punishments for apostasy, such as the dissolution of marriages in cases where an apostate spouse is married to a Muslim, as well as imprisonment, disinheritance, or corporal punishment.
Furthermore, Muslim clerics may issue fatwas declaring believers apostate, putting them at risk for violence at the hands of fundamentalists or even honor killings by their own family members.
The Koran does not call for the death penalty in cases of apostasy, which is why many more moderate clerics argue the death penalty is not sanctioned by God.
However the Hadith - the collected traditions, teachings, and stories of the prophet Muhammad, accepted as a source of Islamic doctrine and law second only to the Koran
- contain several passages supporting the use of the death penalty in cases of apostasy, a response more radical clerics support:
Ibn 'Umar, Az-Zuhri and Ibrahim said, "A female apostate (who reverts from Islam), should be killed. And the obliging of the reverters from Islam (apostates) to repent.
Allah said: — 'How shall Allah guide a people who disbelieved after their belief and (after) they bore witness that the Apostle (Muhammad) was true and that Clear Signs had come unto them? And Allah does not guide the wrong-doing people.
As for such the reward is that on them (rests) the curse of Allah, the Angels, and of all mankind. They will abide there-in (Hell). Neither will their torment be lightened nor will it be postponed (for a while). Except for those that repent after that and make amends. Verily Allah is Oft-Forgiving, Most Merciful.
Surely those who disbelieved after their belief, and go on adding to their defiance of faith, never will their repentance be accepted, and they are those who have gone astray.' (Sura 3:86-90) — Volume 9, Book 84, Chapter 2, p. 42-43."
57. Narrated 'Ikrima: Some Zanadiqas (atheists) were brought to 'Ali and he burnt them.
The news of this event, reached Ibn 'Abbas who said, "If I had been in his place, I would not have burnt them, as Allah's Apostle forbade it, saying, 'Do not punish anybody with Allah's punishment (fire).' I would have killed them according to the statement of Allah's Apostle, 'Whoever changed his Islamic religion, then kill him.'" — Volume 9, Book 84, Chapter 2, Number 57, page 45
58. Narrated Abu Burda: Abu Musa said, "I came to the Prophet along with two men (from the tribe) of Ash'ariyin, one on my right and the other on my left, while Allah's Apostle was brushing his teeth (with a Siwak), and both men asked him for some employment.
The Prophet said, 'O Abu Musa (O 'Abdullah bin Qais!).'
I said, 'By Him Who sent you with the Truth, these two men did not tell me what was in their hearts and I did not feel (realize) that they were seeking employment.'
As if I were looking now at his Siwak being drawn to a corner under his lips, and he said, 'we never (or, we do not) appoint for our affairs anyone who seeks to be employed. But O Abu Musa! (or 'Abdullah bin Qais!) Go to Yemen.'"
The Prophet then sent Mu'adh bin Jabal after him and when Mu'adh reached him, he spread out a cushion for him and requested him to get down (and sit on the cushion).
Behold: There was a fettered man beside Abu Musa. Mu'adh asked, "Who is this (man)?" Abu Muisa said, "He was a Jew and became a Muslim and then reverted back to Judaism." Then Abu Musa requested Mu'adh to sit down but Mu'adh said, "I will not sit down till he has been killed. This is the judgment of Allah and His Apostle (for such cases) and repeated it thrice.
Then Abu Musa ordered that the man be killed, and he was killed. Abu Musa added, "Then we discussed the night prayers and one of us said, 'I pray and sleep, and I hope that Allah will reward me for my sleep as well as for my prayers.'" — Volume 9, Book 84, Chapter 2, Number 58, p. 45-46.
Pay close attention to the fact that moderate and liberal Muslims are being targeted by the extremists. There are at least two very important messages conveyed by this fact, each to a different group. To many of the harshest critics of Islamic extremism, especially conservative Christian critics, this sends the message that Muslims are indeed not monolithic and can’t all be branded as terrorist threats. Muslims are among the biggest direct and indirect victims of Muslim extremism; it does no good to lump these victims into the same group as the criminals.
To the moderate and liberal Muslims, though, this also sends the message that they are not safe, not even in the West, so long as Muslim extremists continue to attract support around the world. They, too, are targets and they will be singled out by terrorists, criminals, and extremists. Standing up for liberal values and against the extremists will likely lead to even more danger, but it’s a price that absolutely has to be paid because keeping quiet will ensure that evil people will win.
Please visit this link. It's quite interesting to read since it contains some Muslims' views on apostasy in Islam.