Before we get started this thread is dedicated to the memory of Terrence Dicks who died yesterday (September First, 2019) at age 84. He was a great writer and script editor and he will be missed.
The Master. The Doctor’s best Frenemy and probably the most popular Who villain that isn’t an entire race of aliens. There have been numerous tales both on-screen and in the EU about the scraps, the two characters get into (as well as several stories where The Master was the star with no Doctor Who around.) In honor of one of the best villains of all time I will be giving my ranking from worst to first of all The Official Masters (that I am aware of)
- Eric Roberts Master (The TV Movie:) This guy is easily the worst incarnation hands down. Not only is Roberts miscast in the role the character himself has been given an array of nonsensical powers (and a snake body!?) to use in his quest to yet again steal the Regenerations of The Doctor.
- John Simm Master (The Sound Of Drums:) I do appreciate the high amounts of homoerotic subtext between Simm and The Tenth Doctor but jeez this guy’s acting is just too much. Simm dials his performance up to 11 (heh) and never comes back down to give the character a chance to breathe.
- Peter Pratt Master (The Deadly Assassin:) The First Extra Crispy Master, Peter Pratt was undone by the ungainly amount of makeup and prosthetics he had to wear to do the role. Also Unlike Beevers a little higher on the list, he didn’t get to do Big Finish Audios where he could act free from the makeup. He does look ghoulish though
- Geoffrey Beevers Master (The Keeper Of Traken:) The second Crispy Master (though not Extra Crispy thank god.) Beevers time on TV was also short and hampered by the makeup. Unlike Pratt, though Beevers has gone on to do phenomenal work with Big Finish in the audio department including the story Master which is one of the finest stories the company has made.
- Anthony Ainley Master (The Keeper Of Traken:) More than just a really good Delgado lookalike Ainley brought his own energy and charisma to the role, playing a slightly cartoonish and over the top Master that contrasted very well with the Doctors he fought with. Also if you haven’t seen his performance in Survival you should. It is amazing.
- Alex Macqueen Master (UNIT Dominion:) One of two Masters (The other is from a noncanonical elseworld) to be invented solely for the Audios. Macqueen plays his Master in a very affable and cultured (but no less evil) fashion. Given a whole brand new set of 13 regenerations from the Time Lords he also lost his fear of mortality and is back to making grand schemes and risky plans. He was so popular they brought him back for the Dark Eyes Quartet of Eighth Doctor Adventures.
- The Roger Delgado Master (Terror Of The Autons:) The first incarnation and the barometer by which all other Masters are judged. Delgado’s Master was the perfect foil for Pertwee’s Third Doctor. The chemistry between the actors of The Master and The Doctor too would go unmatched for decades (Pertwee and Delgado were good friends off-camera) until Gomez and Capaldi appeared on screen together for the first time.
- The Sir Derek Jacobi Master (Utopia:) Only appearing for one episode and under the influence of a chameleon arch Jacobi didn’t get any time for his Master to shine on screen. But, Big Finish hired him as The War Master and there in his own series, Jacobi has proven his Master is one of the best. This Master is absolutely chilling. Able to go from doddering old man to sneering villain at the drop of a hat. Jacobi also plays the long game with his Master deceiving people for years just to get what he wants.
The Michelle Gomez Master/Missy (Deep Breath:) The Heir Apparent to Delgado and my personal favorite version of the character. Missy is a goth and crazy Marry Poppins who just wants to go on adventures and to get her friend The Doctor back (if that involves making a Zombie army of Cybermen then so be it!) Her chemistry with Capaldi is electric as the two bounce off each other and evolve into sort of an uneasy friendship by Series 10. Gomez is also starring in her own series of Big Finish Audios in addition to showing up in one or two of River Song’s adventures 
That’s my ranking. What’s yours? Let me know in the comments and have a happy week Whovians!