The first literary version of this tale appeared as The She-Bear in Giambattista Basile's Il Pentamerone(1634-6). This version of the tale has many variants throughout Europe, but the tale recorded by Perrault several years later has become the most recognized version of the tale.
Perrault's original version of Donkey Skin, originally titled Peau d'Ane, was published in verse form in 1694 and was one of his first literary fairy tales. His more famous collection of tales, Contes du temps passe, would follow three years later. It was later added to his collection in a prose version, paraphrased by an anonymous adapter, which diminished the humor and increased the descriptive elements of Perrault's original. The prose version is the better known of the two (Warner 1994).
Donkey Skin is considered a close variant of the Cinderella tale with many parallels between the stories, especially the theme of the persecuted heroine. While the story was frequently included in fairy tale collections in the late 19th and early 20th century, it was often omitted from popular collections for children in the mid to late 20th century, perhaps due to the incestuous overtones in many of its versions.
The most informative information about Donkeyskin can be found in Marina Warner's From the Beast to the Blonde. If you are interested in this tale, Warner's analysis and comparisons should not be missed.
Note that while the tale is still popular in France with many picture book versions published there, it has slight visibility in the United States and other English speaking countries, perhaps due to its difficult themes of incest and abuse. During a visit to Paris in 2006, a small toy store I visited not far from Sainte-Chapelle had a display devoted to the tale, including a Donkeyskin costume.