Is there an historical reason for this phenomenon? Are these foods sold in different units in other countries? This question was asked two years ago, but received no responses.
To answer the first part of your question, the practice of selling goods such as eggs by the dozen is by no means unique the United States - you'll find the same standard in the UK or France (although they're sometimes broken down into multiples of three - e.g., 6 or 9 eggs).
Why a dozen? In the Western world, there have long been two competing numeric systems (well, more actually, but two have predominated): decimal, or Base 10; and duodecimal, or Base 12. The latter goes back to ancient Mesopotamia, and we still use it when counting time - there are twelve hours in a day, rather than ten, for example. (Twelve was likely chosen because there are twelve months in a year, while ten is useful because we have ten fingers.)
The influence of the duodecimal system is reflected in the cognate terms for dozen that you'll find in most Indo-European languages: "douzaine" in French; "docena" in Spanish; "Dutzend" in German; "duzzina" in Italian; "düzine" in Turkish; "dazina" in Arabic; "dyuzhina" in Russian.
One of the units that the duodecimal system sometimes measured was money. In England, for example, there were 12 pence to a shilling; or in Bavaria there were 12 pfennig to a short schilling. In these cases, it made sense to vendors at a market stall to sell their goods in a bundle for a penny a piece - so a dozen eggs would be worth a shilling.
This standard has since faded away, and nearly all countries have moved toward a decimal monetary system, but the practice of selling goods by the dozen remains - and is a vestige of the old duodecimal system whose roots good back to ancient Sumeria, some five thousand years ago.