I won't lie to y'all: There have been times that I've had too many adult beverages, felt like garbage the next day, and thought about calling out of work. But I've never actually done it. I've come in hungover, but I've never called out of work. I figure, I did this to myself, so I need to put on my big girl pants and push through it.
However, a German court has ruled that a hangover counts as an "illness," (puking, headache, lethargy, and generally feeling like the bottom of a dumpster sure SOUNDS like an illness!) therefore, you should be able to take a paid day off if you're hungover!
I should mention, it's Oktoberfest in Germany, so I'm assuming their decision might've been affected by that!
Good luck telling your boss you'll be taking PTO next time you drink too much!
[BBC]