It is only in Islam where a slave can become Sultan! Because you see, like many other ideologies Islam doesn't promote slavery. Let's discuss Mamaluk Sultanate or in English the Kingdom of Slaves! The mamluk was an "owned slave". After thorough training in various fields such as martial arts, court etiquette and Islamic sciences, these slaves were freed. However, they were still expected to remain loyal to their master and serve his household. Mamluks had formed a part of the state or military apparatus in Syria and Egypt since at least the 9th century, during the Tulunid period. Mamluk regiments constituted the backbone of Egypt's military under Ayyubid rule in the late 12th and early 13th centuries, beginning with Sultan Saladin who replaced the Fatimids' African infantry with mamluks. They were highly committed to their masters, who they often referred to as "father", and were in turn treated more as kinsmen than as slaves by their masters...Their rule lasted from 1250-1570.
Classically in the context of war, the vanquished opponents can be enslaved. Reason Islam has allowed this specific form of slave acquisition is due to the possibility of the defeated converting to Islam after acquaintance with Islamic culture and life without forceful conversion. However today this kind of slave acquisition is not applied anymore and even Islam prohibits it. This is because nowhere in holy Quran or Sunnah (Prophetic traditions) slavery is obligated or recommended but rather emancipation is encouraged and in Hadith selling of free human being has been threatened with (prohibited). On the basis of legal maxim “Custom is an authority” (Al-urf Muhakkima)i, so existence of a custom becomes a law and it's non-existence invalidates it's lawfulness.
Slavery was the norm of the day in the ancient world, a custom, so it was authoritative but today this custom has ceased hence the enslavement in Islamic warfare also ceased. Islam treated slavery as an existing practice (custom) and not an Islamic practice. 194 states of the world have signed UN charter which rejects slavery, and most of the countries have signed anti-slavery treaties. Treaties must be fulfilled in Islamic Law as well.
What holy Quran and Sunnah and the classical jurists dealt with regarding customary slavery were mostly treatment and relationship with the slaves and not promoting slavery. Their works were on reformation of slavery in the ancient world rather than evolution and development of it. Also, today slavery is not allowed in Islam on the basis of the Islamic juristic principles of sad zarae (Blocking the means) and maslaha mursala (continuous interest).
Slavery today will cause massive injustice to women as well as men and mostly they will be treated as sex slaves in the global sex industry and hard labor. In the ancient times slavery was embedded among people's hearts both free men and slaves as they took it as the order of the day, but today slavery has become all that is anti-thesis of humanity. On the basis of reciprocity in international law western powers can also enslave everyone considering the fact that they are in the power and in unjust use of force, always. We must take the view into consideration that Islam did not start slavery but inherited it from the then custom, in fact Islam discourages enslavement and encourages emancipation as has been mentioned. Hadiths of Imams of Ahl Bayt and in Bukhari and Ibn Majah corroborates this point:
“There are three categories of people against whom I shall myself be a plaintiff on the Day of Judgment. Of these three, one is he who enslaves a free man, then sells him and eats this money”.
“Whoever frees a slave, Allah will save all the parts of his body from the Fire, as he has freed the body-parts of the slave”.
Hence slavery was a customary permissible act and it's permissibility was also fixed in a certain scenario of Islamic warfare, but the custom has ceased and hence the permissibility. Enslavement is not the only choice for war captives in Islam, but holy Quran mentions ransom, freedom and forgivenessii. Sheikh Tahir Qadri stated in Peace and Humanity conference Wembley, 2011 “Islam came to abolish slavery through reformations” and cites the verse “And what ye comprehend of the highest good? It is freeing a slave (90:12-13)”. So slavery has ceased in Islam and has become obsolete, ineffective today, on the evidences I have provided.
It is interesting to note that Islam only allowed enslavement in a lawful war, while in that time people were enslaved through hijacking, force, etc. as western colonial powers did for generations. So Islam's enslavement was only valid in one context which was revolutionary in those times. Also Islam came up with numerous ways to free slaves. While in that time there existed only one way to free slave, which is master's wish. So, to say Islam promotes slavery is utterly wrong. Islam's allowance of slavery in the time was only response to slavery being a global custom, so Islam has set forth that time fair and human reformatory laws for slaves something which was like a renaissance. West even with it's renaissance failed to treat slaves like human beings.
But to really ask the question, is slavery in general terms non-existent? If by slavery you mean unbearable suffering restriction of freedom then instead of classic ownership of individual humans, today powerful people and countries enslave nations, its future and its resources. It enslaves all the potential that your country and people can give you. In this sense slavery is very much alive and Islam also prohibits and resists (Jihad) this kind of slavery through it's fair laws of economy, diplomacy, international relations and ultimately war.
i Imam Ibn Nujaim Al-Hanafi & Imam Suyuti Al-Shafi. Ashbah Wa An-Nazaer (in Islamic legal maxims)