The history of what we call dog tags goes back long before World War I

During the Taiping Rebellion in the 1850's, Chinese Imperial soldiers each wore a wooden tag that had their name, age, place of residence, and unit on it.

During the American Civil War, both Union and Confederate soldiers often wrote their names on their clothes, boots, or personal items, or pinned notes with their names or hometowns on them. This wasn't a standardized form of military identification, but a very noteworthy example of what was to come in the United States.

During the Franco-Prussian War in the 1870's. The Prussians made up small tags for each of their soldiers that had their name, unit, and place of residence on them. The soldiers derisively called them "Hundemarken," literally "dog tags."

Dog tags in the United States Army were not officially mandatory (that is, made in a standard form by manufacturers for every soldier) until 1913. Between the end of the Civil War and the beginning of the 20th century, a smattering of many different types of (non-standardized) tags were used.

From the Army Regulations of 1913, with the amendments of April 1917:

(a.) Two aluminum identification tags, each the size of a silver half dollar and of suitable thickness, stamped with the name, rank, regiment, corps, or department of the wearer in the case of officers, and with the name and Army serial number in the case of enlisted men of the Army whenever field kit is worn; one tag to be suspended from the neck underneath the clothing by a cord or thong passed through a small hole in the tag, the second tag to be suspended from the first one by a short piece of string or tape. These tags are prescribed as part of the uniform and, and when not worn as directed herein will be habitually kept in the possession of the owner. The tags stamped as herein provided will be issued to enlisted men as soon as practicable after enlistment or reenlistment, or after entry into active service in the case of reservists.

Sources:

Regulations for the Army of the United States, 1913: Corrected to April 15, 1917 (changes, Nos. 1 to 55) with Supplement Containing Changes Nos. 56-77, Inclusive, United States War Department, Government Printing Office

The Franco-Prussian War: The German Conquest of France in 1870-1871, by Geoffrey Wawro

The Taiping Rebellion 1851-1866, (Osprey Publications) by Ian Heath and Michael Perry

Allow me to follow up on /u/the_howling_cow with an explanation of literal "dog tags."

There's actually a society, the International Society of Animal License Collecting, founded in 1976 by a man named Harry Baker, which is devoted to collecting dog licenses and collating their history. Members pop up frequently in feature articles written by local newspapers seeking the next quirky man-next-door story.

They keep an archive (accessible to members only) of historical data on licenses and associated information. Diane Bandy, a member and past president of the society, has written a number of articles in various publications about collecting, and if you're interested in the topic, you can probably reach out to the society or her.

For a more scholarly look, you might try Phillip Howell's new book At Home and Astray: The Domestic Dog in Victorian Britain, published this year by University of Virginia Press. I don't have it yet, but it's on my list. In 2008, Ingrid Tague of the University of Denver published a paper, "Eighteenth Century English Debates on a Dog Tax," in The Historical Journal. That paper's available on JSTOR for free with an account.

The Beast in the Boudoir: Petkeeping in Nineteenth-Century Paris and Empire of Dogs: Canines, Japan, and the Making of the Modern Imperial World also contain references to the use of dog tags, taxes and licensing.

In any event, the first taxes levied on dogs in Europe appear during the 16th century. The first literal dog tags, showing payment of the dog tax and attached to a dog's collar, date to the 18th century. Dog regulation was a serious matter, particularly as Europe urbanized. Dogs could injure or kill, they consumed food and livestock, and they could spread disease. Culling dogs was the natural solution, but there was no easy way to distinguish a feral or wild dog from one kept as a pet and simply roaming loose. Furthermore, dog culls could be expensive, and a dog tax was a natural way to pay for the mass killing of strays.

In the 1790s, when England was debating its dog tax, fears of hydrophobia (rabies), also called "canine madness" were mentioned in the popular press and in debates within the House of Commons. Proponents of the tax also tied it to hunting and game laws. As early as the 1670s, England restricted the ownership of dogs that might be used for hunting, out of fear that they could be used to poach game. The difference between a hunting dog and a working one ─ one that hauled a dog-cart, for example ─ was narrow and hard to define at times. A dog tax could specifically target the poor, those most likely to poach game.

In the end, England passed a tax that specifically targeted the dogs of the rich and typically allowed the poor to keep their dogs.

In jurisdictions that taxed dogs, the issue of proving that you had paid your tax was an obvious problem. Certificates could be issued, but those didn't travel with the dog. For a dog-catcher culling stray dogs, there was no easy way to determine which dogs were owned and which were wild. The solution, then, was a pot-metal tag, affixed to a collar. Collars are an ancient innovation and have been excavated from archaeological sites thousands of years old. Spiked collars have been used in war; jeweled collars for decoration. The dog-tag, produced en masse with the tools of the industrial revolution, gave the collar another utilitarian function.

The first known tag dates to 1775 in Rostock, northern Germany, while the first known American tag dates to 1853 in Fredericksburg, Virginia. Tags were not universal, even in areas where licensing was common. Paper dog licenses have been found in the historical record in the United States even earlier than that Fredericksburg tag.

With the German states being the first known places to develop a metal dog license medallion, it's perhaps appropriate that they were the first to use a dog tag militarily as well.

As a follow-up, I think I remember reading about soldiers breaking a stick and keeping one half on their person and leaving the other behind. At the end of battle, if any soldier was maimed beyond identification or decapitated, you'd match the two halves together. IIRC, this was in Steven Pressfield's fiction novel "Gates of Fire" about the Spartans. Did he entirely make that up? Or did anyone use such a simple ID tag? Thanks.