In the Wizard of Oz (the movie version) the Good Witch of the North, Wicked Witch of the West and Wicked Witch of the East are all mentioned.
Was there ever a Witch of the South?
If you are talking about the 1939 film, no Witch of the South is mentioned. I searched the movie script online and no instance of "south" was found. In the film, Glinda is the Good Witch of the North. In the book, Glinda is the Good Witch of the South. In the film, Glinda performs the functions which the book's Good Witch of the North performed.
In the 1939 film version of The Wizard of Oz, Glinda is the Good Witch of the North, not the South as in the book. She is played in the film by Billie Burke. Glinda performs the functions of not only the novel's Good Witch of the North and Good Witch of the South, but also the novel's Queen of Field Mice, by being the one who welcomes Dorothy to Oz, sends her "off to see the Wizard," and orchestrates her rescue from the deadly poppy field in addition to revealing the secret to going back home.
If you are talking about the books, Glinda is the Good Witch of the South. There is a Good Witch of the North, but she is not very fleshed out.
She appears in Chapter 2. The Council with the Munchkins.
A description of her appearance:
Three were men and one a woman, and all were oddly dressed. They wore round hats that rose to a small point a foot above their heads, with little bells around the brims that tinkled sweetly as they moved. The hats of the men were blue; the little woman's hat was white, and she wore a white gown that hung in pleats from her shoulders. Over it were sprinkled little stars that glistened in the sun like diamonds. ... But the little woman was doubtless much older. Her face was covered with wrinkles, her hair was nearly white, and she walked rather stiffly.
Explaining the existence of the four witches:
"But I thought all witches were wicked," said the girl, who was half frightened at facing a real witch. "Oh, no, that is a great mistake. There were only four witches in all the Land of Oz, and two of them, those who live in the North and the South, are good witches. I know this is true, for I am one of them myself, and cannot be mistaken. Those who dwelt in the East and the West were, indeed, wicked witches; but now that you have killed one of them, there is but one Wicked Witch in all the Land of Oz--the one who lives in the West."
Here is a 1900 illustration of the Witch of the North from the book:
Wikipedia has this to say about her:
The Good Witch of the North is a fictional character in the Land of Oz, created by American author L. Frank Baum. She is the elderly and mild-mannered Ruler of the Gillikin Country. Her only significant appearance in Baum's work is in Chapter 2 of The Wonderful Wizard of Oz (1900), in which she introduces Dorothy to Oz and sends her to meet the Wizard, after placing a protective kiss on her forehead. She makes a brief cameo appearance at Princess Ozma's birthday party in The Road to Oz (1909), but is otherwise only mentioned elsewhere in the series.
The good witch of the south is Glinda in the books. In the movie they are combined in the book the good witch of the north is at the beginning when Dorothy gets the shoes but Glinda is at the end and tells Dorothy how to get home. so in the movie she is the basically two different witches both north and south.
In the book, there's not problem about that, as said before. But in the movie, we have indeed only — Glinda, "Good" Witch of the North — The Wicked Witch of the West (she hasn't got any name, while some spin-off named her "Elphaba" or "Theodora"). — The Wicked Witch of the East (she is the sister of the Wicked Witch of the West, and may also be Miss Gulch, as I'll explain later).
There is a very famous theory explaining that there's no Good Witch at all in Oz: Glinda is actually a manipulator, who lies to the Munchkins (who are very innocent) and to Dorothy, and wants Dorothy to kill the other witches and wizards of Oz to rule alone, and that you can read here:
It is not said in the page I mentioned here, but Glinda could have already killed/exiled the Witch of the South when Dorothy arrives in Oz.
Then, I'll talk about my idea about the witches. There is only ONE evidence in all the film which could prove that Oz is actually Dorothy's dream, if this scene wouldn't exist there would be no problem. It is the scene where she sees Miss Gulch from her window during the tornado, and when she transforms into the witch. …did I say, "The Witch" ? Certainly not: into a witch. Because, she looks like the Wicked Witch of the West, but, her clothes are GREY instead of BLACK. Then, let's think that Oz is on the west from Kansas. Then, for Oz, Miss Gulch may very well be the "Wicked Witch of the East, couldn't her ? A witch that transforms into her real witch form when she enters in Oz, but who is simply a rich lady when she's in Kansas. Also, she flies around the house in that scene. That's not very careful, that may be the cause why she was eventually… crushed by the house. You must notice that all the look alike of the Oz people appear near Dorothy's bed at the end… all of them, except Miss Gulch. Perhaps because she's dead ? That she's right under their feet… under the house ?
Also, Miss Gulch's name is given in the book as Almira Gulch. And all the names of the other witches in the different spin-offs are also in —a (GlindA, TheodorA, ElphebA…)
Yes, I know that doesn't fit with the book. But that fit with the film.
For those that haven't bothered to do their research:
Original Oz books by L. Frank Baum
Wicked (Book and Musical)
Oz the Great and Powerful movie
None of these universes coincide. Often, Glinda is referred to as the Good Witch of the North since that character appears very briefly in the original book.
Now, obviously, Galinda is the Good Witch of the North. Elphaba is the Wicked Witch of the West. But, in Oz the Great and Powerful (2013) movie, is is shown that Theodora, sister to Evanora, most likely the Wicked Witch of the East, is at first Good, but her sister, who is evil, makes her eat an apple making her show her wicked side. She is then changed to look like the Witch of the West that we all know and hate. It should be noted that when Theodora is crying, the watery tears burn her cheeks and she pleads with her sister to stop the pain. This is much like the water Dorothy throws onto the Witch of the West, (Theodora but now Elphaba). In the movie, Galinda states that she is the Good Witch of the South, not the North. This is odd, seeing as that the Graveyard she is first seen at and her kingdom is to the north of the Emerald City. There was never a show of who is or will be the good witch of the North. This is assumably Galinda, as in the Wizard of Oz movie, but then who will be the Witch of the South? We may never know. But if director Sam Raimi is continuing the series, we may find out in either of the other movies. My assumption is that the Wizard himself has taken over the south for Galinda, or that the true Witch of the South is actually Dorothy herself. Seeing how she is from the south, Kansas, that may be the reason that she was brought to Oz in the first place.
I haven't read the original books of Oz. I know there is a good witch of the south in one of the books, from what I read on some blogs. However, when I just view the film, I come to the conclusion that Dorothy is the good witch. She's from the South (Kansas) and she certainly does many good deeds. We do see the the bad witches from East to West. The good which from North and the good witch from the South being Dorothy.
Well that's my take on it.