Russian is my native language, I remember several of these from my childhood. The Tale of Tzar Saltan, Baba Yaga, Father Frost, Ilya Murometz, Sadko, Princess Frog.
Popular Russian folk tales include Kolobok (small yellow bread-like being), Vasilisa the Beautiful (beautiful and wise girl), as well as Brother and Sister (not to be confused with Grimm's Hansel and Gretel).
Most of the popular folk tales in Russia involve Baba Yaga, a witch who lives in the forest. In most stories she tricks foolish young girls into housework for her.
The first two that come to mind are Baba Yaga and Rusalka. I can also fainlty recall one being told to e by my mother about a golden ring. Perhaps we could find a medium and ask her to contact the spirit of Vladimir Propp?
The Russian tale I'm most familiar with is Baba Yaga. It's a story about a wicked stepmother who sends the daughter to see an aunt who is actually a witch. The girl outwits the evil witch and tells her father about the ordeal. Her enraged father then kills the stepmother!