This one made me go, "Ha! Take that, everyone who uses the word I don't like!" ;-)
See, I was always a normality girl. But more and more often I'd begun hearing normalcy. And it drove me batty. Here, my friends, is why.
Normality itself is a relatively new word, entering the written world of English in only 1849. It most likely came from the French normalité, which became a borrowed word in 1834. Meaning exactly what you'd expect.
Normalcy, however, dates from 1857. And what, you ask, did it mean? "Being at right angles." It's a mathematical term! In the 1920s President Harding used it in place of normality in a speech describing the political situation and was liberally made fun of for his incompetency with speaking. Since then it has edged its way in more and more, but "the normality."
So there. ;-)