The OP's question is based on some implicit assumptions which need to be addressed - that of treatment of slaves (which is separate from the institution of slavery as usually understood today).
Had the slaves not been mistreated in non-Islamic countries, it is unlikely they would have revolted/demanded their rights or that anyone would have exerted enough pressure on the governments of these countries to force them to finally abolish slavery in the first place.
The OP's question assumes that the slavery in Islam is the same as that practiced by Godless colonizers or corporations or individuals who - when they take slaves - be they sex slaves, or debt slaves or slaves of personal assistance and physical labor - treat them as sub-human. The only slavery existent in Islam (which sets policies to end that as well) is that of labor and assistance. The other forms of slavery which are rampant today throughout the world including the developed world, are prohibited. As for physical/personal assistance, unlike the generally understood concept of slavery the questioner may be used to, masters in Islam are not "superior" to slaves anyway, neither are they ever allowed to mistreat their slaves.
'Your slaves are your brothers upon whom Allah has given you authority. So, if one has one's brethren under one's control, one should feed them with the like of what one eats and clothe them with the like of what one wears. You should not overburden them with what they cannot bear, and if you do so, help them (in their hard job).' (Bukhari)
Further, the respect of a slave is such that the Prophet (S) prohibited the master from even calling to the slave using the word "slave". In another Hadith, "Whoever beats the slave or Servant unjustly, revenge will be taken from him on the Day of Judgment." We are commanded to consider them as are equals, and regardless of whether we are slaves or masters, Muslims are constantly reminded that we are all slaves on earth to our One King, God. "Be slaves of God, brothers", said the Prophet (S).
Slaves in Islam have legal rights as well - with plenty of leniency. If slaves commit crimes, their punishments are half of those of a criminal who was a free person. When asked how much the mistakes of slaves should be forgiven, the Prophet (S) said "seventy times" - meaning that even when mistaken, slaves should be treated with kindness. With the respect that masters are demanded to give their slaves in Islam, slaves are also required to respect and serve their masters back. And why not? When they are fed, sheltered, clothed, respected, often educated and treated as one of their own by their masters? In a Hadith, "When a slave or servant is faithful to his master and also worships his Creator, he is deserving of a double reward (in the hereafter)."
So before questioning the idea of abolishing slavery in Islam, one should first recognize that the only slave-master relationship allowed in Islam is that of respect, loyalty, love and protection, and even cooperation in the work, if it is hard work. The slave-master relationship is absolutely not the one that today's non-Islamic countries conceive it to be, based on their own historical realities.
With the Islamic treatment of slaves, it is unlikely that slaves would revolt against their masters or that others would rise up on their behalf in the first place, in the kind of uprisings seen in non-Islamic countries. Why would such a thing happen if slaves were not being abused in the first place?
Despite demanding this respect for those under one's service, Islam still sets policies towards a slavery-free world. The act of setting slaves free is important enough in Islam for there to be more to it than simply "abolishing slavery".
'A bedouin came and said, 'Prophet of God! Teach me an action which will enable me to enter the Garden.' He said, "The question is a broad one, even though you have asked it in only a few words. Free someone. Set a slave free.' He said, 'Are they not the same thing?' 'No,' he replied, 'Freeing someone is setting someone free yourself. Setting a slave free is to contribute to the price of setting him free...' (Bukhari)
The Quran and Hadith give several ways that Muslims should "free slaves".
- Freeing a slave is one of the highest virtues in Islam, mentioned over and over again as
simply a beautiful that should be done for the sake of itself, for God.
- Freeing slaves (as someone mentioned above) has also been set as the penalty to be paid
for certain sins in Islam (such as breaking oaths, or making up to your wife after certain marital problems, etc.)
- Slaves (especially slave girls) are encouraged to be married out of slavery.
- Slaves have the right to ransom themselves out of slavery.
- Freeing a slave in Islam is not as simple as heartlessly placing a "ban on slavery", because in a world where
slaves are skilled in a specific labor - then banning slavery doesn't
do much for them. Having spent years in someone's service,
most have nowhere else to go and nothing else to do anyway. Hence freeing a slave in Islam
means giving them a new life, and then freeing them to it. That
would include providing them with education, vocational training,
wealth, marriage, and more.
Since Islam is a universal religion which must be practical in all times and all ages, it does not make statements which are unreasonable in certain communities or for some people. For example, as it was in Arabia at the time that the Quran was revealed, with so much of the agriculture and livelihood being based on the work of slaves, abolishing it could likely bring the economy to a grinding halt - and what of food and sustenance for everyone else? Hence rather than proclaiming it outlawed in one step, the approach taken was more practical and humane. For another example, if certain individuals are unable to take care of themselves or for any other reason really need permanent assistance, it would be unfair or impractical for them to be considered sinners because they took slaves, despite their good treatment of them.
In addition to this answer, I recommend you to view the slavery related issue being discussed at 22:35 here: http://www.youtube.com/watch?v=j-uHDxm1oHE
Again, do keep in mind that countries such as Oman, UAE, Saudi Arabia etc are hardly "Islamic" countries. The majority population in these countries happen to be Muslim, but the laws that are practiced are not all Islamic, they are cherry-picked to suit the rulers' convenience.