I originally posted this on the Anime & Manga Stack Exchange site. Below is an updated and improved version for your enjoyment.
The first ‘magical girl’ anime was Sally The Witch, who transformed with a wand into another costume – This was a simple animation though and performed in the same cut as the rest of the scene. Sally The Witch came out in 1966 and was in black and white. It still has significant fan-following – no doubt helped because of its historical significance. The latest edition of Sally the Witch was a feature-length film in 1990 – with upgraded aesthetics.
Sally magically changes her clothes
Newer releases contained colour and special effects unavailable to anime production in 1966
However, that makes this post too short, so for addition information let’s look at the anime Cutey Honey which was released in 1973. Cutey Honey was much more focused on the transformation scenes of the heroines and began many of the transformation tropes which have lasted to this very day – activation words (“HONEY FLASH”), nudity whilst transforming, floating around the screen while transforming, etc.
Surprisingly though, Cutey Honey was not a shoujo, it was a male-targetted show and the characters were seen at the time to be superheroes rather than magical girls. However, Cutey Honey was a significant influence on transformation scenes from then on and looking back at the show, it’s surprising to think that they are not actually magical girls. They even have their own love-based catchphrase, reminiscent of later famous magical girl shows such as Sailor Moon:
“Stars in the heavens! Flowers on the Earth! Love to the people! Warrior of Love! I am Cutey Honey!“
(partial sequence sped up)
Cutie Honey is a much bigger deal in Japan than it is in the US and the rest of the West. This is primarily due to it not being available in English on home media until Discotek released it in 2013.
Some of Cutey Honey’s transformations
As anime was still relatively new and novel, there weren’t a high volume of series airing at one time, unlike the current range of airing shows each season. In between Sally the Witch and Cutey Honey, there was only one other qualifiable magical girl anime – Himitsu no Akko-chan, who transformed similarly to Sally the Witch, albeit with a mirror instead of a wand.
Newer versions of Himitsu no Akko-chan were also released, the latest being in 1998
If you’re interested in transforming robots too, check out this question.