Apostasy as a Capital Crime

Leaving Islam is a capital crime according to the ahadith (that's the plural of hadith which refers to recollections of various sayings and events during Muhammad's life, or the lives of the Rightly Guided Caliphs). For anyone who wants to know some specific references where death is mandated for apostates here you go:

Ali burnt some people and this news reached Ibn 'Abbas, who said, "Had I been in his place I would not have burnt them, as the Prophet said, 'Don't punish (anybody) with Allah's Punishment.' No doubt, I would have killed them, for the Prophet said, "If somebody (a Muslim) discards his religion, kill him."

From Sahih Bukhari Volume 4, Book 52, Number 260
If you are having trouble with the link then cut and paste this:
http://www.usc.edu/dept/MSA/fundamentals/hadithsunnah/bukhari/052.sbt.html#004.052.260

Or This from Volume 4, Book 52, Number 261:

Eight men of the tribe of 'Ukil came to the Prophet and then they found the climate of Medina unsuitable for them. So, they said, "O Allah's Apostle! Provide us with some milk." Allah's Apostle said, "I recommend that you should join the herd of camels." So they went and drank the urine and the milk of the camels (as a medicine) till they became healthy and fat. Then they killed the shepherd and drove away the camels, and they became unbelievers after they were Muslims. When the Prophet was informed by a shouter for help, he sent some men in their pursuit, and before the sun rose high, they were brought, and he had their hands and feet cut off. Then he ordered for nails, which were heated and passed over their eyes, and they were left in the Harra (i.e. rocky land in Medina). They asked for water, and nobody provided them with water till they died.

The website where you can read these two ahadith is a complete collection of Bukhari, so do a word search when you get to the page. Both references are quite a ways down the page.

The most important text of course is from the Quran itself (16:106):

Any one who, after accepting faith in Allah, utters Unbelief,- except under compulsion, his heart remaining firm in Faith - but such as open their breast to Unbelief, on them is Wrath from Allah, and theirs will be a dreadful Penalty.