I don't remember if I ever had a "standard" midnight snack, either when I was a kid at home or in later years.
Nowadays, if I'm hungry late at night, it could literally be anything, including some kind of leftovers. Most often, though, I guess it's some kind of chips (usually tortilla chips) or, when I'm being bad and have any in the house, cookies. The problem, of course, is that there's no such thing as an actual snack portion. My brain might understand that concept, but my stomach doesn't. Just gimme the bag.