Is there a button in iTunes to say "Stop after playing this song"? Because I might just want to go to bed after this one song (but don't want to stop it midway – It's a classic).

Edit: Found a workaround in iTunes 11, a two-click solution but it works. See my answer.
iTunes 11

Click on the Up Next button and press clear. It will stop after the current song regardless where you start the song from.



iTunes 12

"Clear" is at the end of the Up Next list, rather than the top, so you'll have to take the extra step of scrolling to the bottom.