I seem to remember he lived around the 16th century.
The most notable one was Pargalı Ibrahim Pasha, he was the Grand Vizier of Suleiman the Magnificent.
He was given immense power, such as appointing generals and other viziers, making treaties, coining money etc.
He was like a prime minister if you compare to the modern age.
Though this was not asked in the question, I would like to start with the basics just to explain that they were not slaves at all. For the first half of the Ottoman Empire's lifetime, the devşirme system worked well and very effectively. A boy who was picked by an official to become a part of the Ottoman elites was getting a first class education and could serve in almost every position -janissary, vizier, architect, naval officer... Of course, for him there was no way to become the Sultan. With this little exception, he could serve in anywhere. And the highest position he could get was Grand Vizier -second to only Sultan himself.
Probably the most important figure among devşirme Grand Viziers is Sokollu Mehmed Pasha. He was born around 1506 and was Grand Vizier between 1565-1579, during which he served three different Sultans, including Suleiman I. He is well known -for lots of things, but especially- for his answer to Venetian ambassador after the Battle of Lepanto (which Ottomans lost):
"By conquering Cyprus we have cut off one of your arms; at Lepanto by defeating our navy you have only shaved off our beard. However, you know that a cut-off arm cannot be replaced but shaved-off beard grows thicker."
The answer alone shows the efficacy of the Ottoman system before being corrupted.