Yom Mem v'Mem (Commonly known in the Diaspora as M&M Day):
In 5777, begins 14 of Tishrei at sunset (this year, 16 October). Generally begins on 11 of Tishrei (this year, 13 October). It is the most complicated holiday on the Jewish calendar, due the myriad of days on which it cannot fall.
When it falls on Isru Yom Kippur, as it did this year, it is postponed to the next day, although some Rabbis will break their fast with M&Ms (a shehechiyanu is not said, however). But Yom Mem v'Mem should not observed on a Friday. Simply put, the commandment to eat M&Ms will interfere with preparations for Shabbat.
Neither can it fall on a Shabbat, however. The prohibition against observation on Shabbat is thought to have stemmed from the tradition of eating meat on Shabbat, and the fear of encouraging the mixing of meat and milk. However, modern historians point to an obscure Rabbinic text that explains how when the Jews offered their Shabbat sacrifices in the time of the Temple, the smell of the sacrifice would mix with the smell of the sweet dairy chocolates, and the people of Israel would think that meat and milk was being mixed!
Some Jews will indeed observe it anyway on Shabbat, noting that their enjoyment of M&Ms as a way to "delight in Shabbat," (Isaiah), citing the Shulchan Aruch: Rather, since it is assumed that most people take more pleasure in eating meat than in other foods, and in drinking wine more than other drinks, therefore they should increase in [consuming] meat and wine according to their means. These Jews simply take more pleasure in eating M&Ms than any other food.
However, for most tradition Jews the world over, the holiday this year will fall on 14 Tishrei, beginning Saturday night and extending into Sunday. It's clever timing, really: many Jews will be building their Sukkot, and Yom Mem v'Mem will make it even sweeter!