Well there are various differing legal opinions. In the Hanafi madhab, the main view is that apostasy is not punishable by death, only if an apostate commits treason against the state otherwise it's not punishable, since the view is that faith is held accountable not in this world but in the akhirah (hereafter).
Well it doesn't need much hadith or Islamic jurisprudence because it's quite clearly advocated in the Qur'an:
"Let there be no compulsion in religion: Truth stands out clear from Error: whoever rejects evil and believes in Allah hath grasped the most trustworthy hand-hold, that never breaks. And Allah heareth and knoweth all things." 2:256
Some commentators believe the above first is abrogated but some do not. Furthermore the next verses make it pretty clear - death is not a punishment for apostasy (it has none):
"Those who believe, then reject faith, then believe (again) and (again) reject faith, and go on increasing in unbelief,- Allah will not forgive them nor guide them on the way" 4:137
Quite clear evidence that there were Muslims & non-Muslims who believed, converted away, believed again etc etc - and they were allowed to do so. If the punishment for apostasy was death - they'd never have had the chance to revert.
"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.
This because they love the life of this world better than the Hereafter: and Allah will not guide those who reject Faith.
Those are they whose hearts, ears, and eyes Allah has sealed up, and they take no heed.
Without doubt, in the Hereafter they will perish." 16:106-109
Self-explanatory.
But the most obvious verse on the apostasy issue & the most used to paint a negative portrait on Islam and probably the most quoted out of context verse also reaffirms the main Hanafi position:
"
They but wish that ye should reject Faith,
as they do, and thus be on the same footing (as they): But take not friends from their ranks until they flee in the way of Allah (From what is forbidden).
But if they turn renegades, seize them and slay them wherever ye find them; and (in any case) take no friends or helpers from their ranks;
Except those who join a group between whom and you there is a treaty (of peace),
or those who approach you with hearts restraining them from fighting you as well as fighting their own people.
If Allah had pleased, He could have given them power over you, and they would have fought you: Therefore if they withdraw from you but fight you not, and (instead) send you (Guarantees of) peace, then Allah Hath opened no way for you (to war against them)." 4:89-90
Off the top of my head - these are the logical proofs I remember reading a while back. The above verse makes it quite plain - it talks about the occasion when some Muslims were apostates - the verse prior gives some more clarification on the topic:
"Why should ye be divided into two parties about the Hypocrites? Allah hath upset them for their (evil) deeds. Would ye guide those whom Allah hath thrown out of the Way? For those whom Allah hath thrown out of the Way, never shalt thou find the Way." - 4:88
Those who turned 'renegade' or against the Muslim community at the time were commanded to seize them & kill them - however the command made exception to apostates who were peaceful & did not wish to go against the Muslim community - 4:90.
That verse from 4:88-90 - explains or clarifies the Hanafi position as well as most Muslims on apostasy. In fact line for line those two verses explain & clarify the hanafi position on apostasy.
There is one glaring problem with those who follow the belief that apostasy is punishable by death - one of the hadiths used to deduce so, is seriously flawed. The one related by Ikrimah has multiple hadith all with slightly different stories on the incident regarding Ali (ra) making it very unreliable. But the most noteworthy thing which is wrong with that hadith is (a) it implies that Ali (ra) did not know the ruling regarding apostasy (kind of crazy to imagine) since in one of those versions of the same hadith he burnt apostates, (b) it implies that ibn Abbas knew more about Islam than Ali (ra) - extremely hard to believe, even more so when Abbas was 10 years old when he converted and 13 when the prophet (saw) passed away. Not to mention some hadith compilers thought of Ikrimah as a weak chain & a liar - this is why this hadith is not in Muslim.
http://islamicperspectives.com/punishmentofapostasy_part2.html
The above link highlights the problem with the hadiths that support punishment by death.
