Buckle in, travelers, we're cranking open the neon-humming door of the Takeout Time Machine. Its buttons are sticky with soda pop syrup, and inside it hums the faint, sugary static of days gone by.

Before there was a Starbucks on every corner, time-crunched Americans could get a quick caffeine fix straight from their office vending machines. But nowadays, coffee vending machines offering piping ...