What institution better captures the intense, work-obsessed individualism of American life than the high-end coffee shop? Walk into a Starbucks, Peet’s or some boutique cafe and you encounter people hunkered down with their brews and their screens or busily hurrying to their next appointment. The coffee shop is now an extension of the office cubicle and the college library. Boring.

But it wasn’t always that way. Coffee shops were born as raucous, free-spirited, slightly disreputable places—a bit of history that might help...