The Doomsday Algorithm
Doesn't that sound like a thriller title? But no, it's a method for calculating the day of the week for any date that you can do in your head. Invented by John Conway (creator of the game Life, among many other things) and streamlined by various other people. I'd heard of it before, but it always sounded too complicated; but the web page lays it out nicely.
I'm still more likely to use a calendar, though, just to be sure. I was very pleased a few years ago to discover that the calendar built into emacs could tell me when Ramadan would be in various years in the 23rd century.