Hallowe'enie
That's how they used to spell it when I was a sprat. That spelling was insisted upon, in fact; any other way--the other way, I suppose--was red-penciled.
The reason it's "Hallowe'en" and not "Halloween", we were told, is that the word is a contraction, and contractions contain apostrophes. Why? They just do. Sit up straight, put down that protractor, and pay attention.
"Hallowe'en" is a contraction of "All Hallows' Evening". Nowadays we know "hallow" only as a verb meaning "to revere" or "to make holy" and as its adjectival form "hallowed", so "hallows'" looks strange, but the word began life as a noun meaning "holy man" and later "saint", from an Indo-European root that also gave us, eventually, "whole" and then "wholesome" and also "hale" (both meaning "healthy" in slightly different ways), as well as "holy". (Didn't you always suspect that "holy" and "wholly" were related somehow?)
All Hallows' Evening, then, was the night before All Hallows' Day, or All Saint's Day. In Celtic times, the last day of October--which is to say the last day of fall and also the last day of the Celtic new year--was when the spirits of the dead could walk the earth, getting rather ineffectual vengeance by playing tricks; the living made offerings of food to the spirits as a bribe or dressed like the dead to fool them into leaving the living alone. Christianity, as it did with Christmas, Easter, and a few other holidays, appropriated these traditions as a way of convincing the heathens to convert--"See? We're just like you!"
So: All Hallows' Evening becomes All Hallows' Even--a Middle English abbreviated form which is unrelated to the other "even", meaning "tied" or "level"--which becomes Hallows' E'en and finally Hallowe'en. The apostrophe-less spelling, I admit, is pretty old, too, and there's lots of precedent--Robert Burns used it; but the word is a contraction, that apostrophe has every right to be there, and I think it looks nicer. Plus, "Hallowe'en" is indisputably correct, which is always nice.
Do schools still do any of what they did when I was a child? Red-penciling, insistence upon correct spelling, and explanations of why the correct is correct and any other way isn't? If they don't, then I can't help but think that they're shirking their duties. I know life has become a little more complicated in the last few decades, what with having to scan the tots for guns and teach them about condoms and such, but there still ought to be enough time left over to teach children the elements of the language they speak.