It's not entirely true that the Siesta is exclusively a staple of Spanish culture. Rather, I do believe it's well-known in the United States precisely because it has been exported to Spanish colonies. The Siesta also has equivalents in many mediterranean cultures. The one I'm most familiar with is Italy, although I'm also aware of a similar phenomenon in Greece. But for this answer I'm going to tap into my rather esoteric knowledge of the history of Italian labor and labor relations.

Interestingly enough, in a 2009 survey about half of Spaniards interviewed reported never taking a Siesta over the course of their day. Increasingly, the rigors of the modern economy makes taking a siesta impractical. However, this doesn't mean the siesta hasn't had a lasting impact on the "Mediterranean" lifestyle: in many workplaces, a break to go home and take a nap has merely morphed into a long lunch hour. Rather than nap, many workers use their long lunch hours to run errands, or visit to exhibitions, or otherwise relax. In Italy, the equivalent of the Iberian Siesta has various regional names: Pennica, Pennichella, Pisolino, and Pisolo. While the act of taking a small break during the hottest hours of the day (ubiquitously after lunch) has multiple names, in the hot southernmost parts of Italy the very time of the day when "Nap Time" takes place also has its own name: the controra. In Italy, as in Greece, historically the controra has been associated with superstitions involving nymphs, demons, and other malicious spirits. Italians also have a word for the tiredness and sleepiness that normally sets in after a meal: abbiocco, and the word has its regional variants as well, like cecagna (typically heard in and around Rome). The time taken for the pennica can also vary, from fifteen minutes to one or two hours, based on individual preferences and the demands of different jobs. Interestingly enough, if you look into the etymologies of the various "nap words," many date to the second half of the 20th century, indicating that perhaps only the rigors of modern lifestyle have made it necessary to precisely define what was otherwise a normal part of the day.

The afternoon nap is an especially enshrined right of shopkeepers, who to this day sometimes take an afternoon break long enough to travel home and eat lunch with their families. Many local ordinances, the most stringent of which were adopted in the "austerity" of the 1970s, even limit the total amount of hours that shops can stay open. So shopkeepers also use a midday break of several hours to extend their opening time early in the morning and late into the evening. Children up to elementary school age are also encouraged to take naps, with many schools following a six-day weekly schedule with lessons from 8 in the morning to 1. Under this system only one or two days a week would be designated as "full days" where students would be expected to attend lessons in the afternoon, although since the mid-1980s the growing proportion of dual-income households has forced this to change, first with after school activities, and increasingly by implementing 8 AM-to-3 PM school schedules.

The afternoon nap is also en enshrined right of office workers, even though they are typically expected to be at their workplaces more or less continuously during business hours. According to law, workers cannot be fired while on the job if they are merely napping and not in deep sleep (un profondo assopimento are the precise words, however how that would be determined is anyone's guess).

In Italy as in Spain, the afternoon nap has been suffering a slow but steady decline. Air conditioning has eliminated the need to stop working during the hottest hours of hot summer days (as long as workers are in an enclosed space). The industrialization of the economy has tied breaks to the rhythm of the assembly-line and laws regulating mandatory rest periods. Office workers are expected to be responsive at all times, so lunch breaks have been getting shorter. Since the early '90s, shopkeepers in cities frequented by tourists have found strong incentives to stay open during the middle of the day, as tourists are unlikely to want to return to their hotel rooms during daylight hours. Retail chain stores also stagger shifts in order to stay open. In order to keep pace, some shops (especially those in downtown areas) sometimes advertise an "Orario Continuo," meaning they do not close in the middle of the day.