Full list based on Wookieepedia, Quora and extensive Googling of other sources. "{}" shows canon sources for the information about apprenticeship.

* [Darth Maul][1] { *Episiode I* }
* [Vergere][2] { *Legacy of the Force: Betrayal* }
* [Darth Tyranus/Count Dooku][3] { *Episode II* }
* [Garth Ezzar][4] { *[Destruction RPG](http://starwars.wikia.com/wiki/Destruction_%28Living_Force_adventure%29)* }
* [Darth Vader/Anakin Skywalker][5] { *Episode III - VI* }
* [Ferus Olin][6] (informal apprentice) { *The Last of the Jedi: Secret Weapon* }
* [Lumiya][7] { *Jedi vs. Sith: The Essential Guide to the Force* }
* Luke Skywalker when Palpatine was in clone body { *Dark Empire 5: Emperor Reborn* }

Please note that aside from Maul; Tyranus and Vader, none of these are Disney Canon - they are all Legends canon only.

All 3 Disney canon apprentices had apprentices of their own (Maul: Savage Opress; Tyranus: [a whole bunch][3]; Vader: [a whole bunch][5] but IIRC none are Disney canon). It's not clear if Savage Opress strictly violated the Rule of 2 as they didn't meet until after Maul was de-apprenticed by Obi-Wan's lightsaber.

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He also had a bunch of people he trained who were not strictly speaking "Apprentices", such as (incomplete list of examples)

* Emperor's Hands (e.g. [Mara Jade][8])
* Prophet [Cronal][9] etc.
* Adepts who weren't apprentices, e.g. an [unknown Nikto][10]  { *Book of Sith: Secrets from the Dark Side* }


  [1]: https://starwars.fandom.com/wiki/Darth_Maul
  [2]: https://starwars.fandom.com/wiki/Vergere
  [3]: https://starwars.fandom.com/wiki/Dooku
  [4]: https://starwars.fandom.com/wiki/Garth_Ezzar
  [5]: https://starwars.fandom.com/wiki/Anakin_Skywalker
  [6]: https://starwars.fandom.com/wiki/Ferus_Olin
  [7]: https://starwars.fandom.com/wiki/Lumiya
  [8]: https://starwars.fandom.com/wiki/Mara_Jade_Skywalker
  [9]: https://starwars.fandom.com/wiki/Cronal
  [10]: https://starwars.fandom.com/wiki/Unidentified_Nikto_dark_side_adept