Early on all libraries were non-circulating libraries, and cards identifying users were unnecessary. With the public library movement in the 19th century, it became necessary to register users who were permitted to borrow books. Initially this was done with cumbersome ledger systems, with each page representing a borrower and the books borrowed (and returned) listed.
According to Helen Thornton Geer, in the book, "Charging Systems" (Chicago: ALA, 1955), in about 1900, John Cotton Dana, director of the Newark (N.J.) Public Library, devised a system using a borrower's card and a book card. These early borrower's cards were not the simple identification cards of today, but rather a card with space to enter the date borrowed, date due, and date returned for each book circulated. As such they did fill up and the "Detroit system" of an identity card was developed by Ralph Ulveling in 1929.
In 1932, Gaylord Brothers introduced an electrically operated book-charging machine, using the basic two-card system devised by Dana. This system used a borrower card with a metal plate with an embossed number to register the borrower's identity onto the book card, which was filed by call number.
Through the following decades, various other machine-assisted and automated systems were developed, and circulation systems are now a key part of integrated library systems (ILS)--Geer's book, cited above is a guide to the advantages and disadvantages of the systems in use in 1955. The metal plate has been replaced with a bar code in modern systems.
Older systems, some of which are illustrated in the blog posts below, assigned each borrower a number which remained on the book card kept in the library book. With modern circulation systems, the borrower number is recorded only in the circulation system itself, and is disconnected from the book record once the book (or other library item) is returned, thus enabling compliance with ALA's "Policy on Confidentiality of Library Records."
A number of library cards in the US is one statistic that isn't collected for the federal public library survey series, "Public Libraries in the United States," by the National Center for Education Statistics of the U.S. Department of Education. Neither does a number appear in the "Bowker Annual." There's a hesitation to collect and present such numbers, due to the fact that the accuracy of them would vary from library to library.
For example, ALA publishes its own annual public library survey, through its Public Library Association (PLA, a division of ALA), the "Public Library Data Service (PLDS) Statistical Report," which is conducted on a random sampling of 1,000 public libraries all over the US, all of various sizes and locations. The survey questionnaire does ask each library to provide its number of "library registrations" but with the caveat: "Report this figure only if the library has purged its file at least once within the last three years. If not, indicate by putting N/A in the space." Many of the participating libraries, which are individually named in the report, do provide a number, but dozens of them do not. People move away, or pass away, and, to put it frankly, citizens are under no obligation, legal or otherwise, to inform the library of their own or any relative's status and its effect on the library’s number of registrations. In short, the number of library cards in the US is a statistic that doesn't exist.
How widely a library card may be used also varies by jurisdiction. Over the years, public libraries have made great strides in resources sharing, through the development of inter-library lending procedures, cooperative partnerships, regional networks, and even some statewide networks. But a single all-state borrowing card and system would be difficult to develop, though there are successful statewide and extensive regional networks for reciprocal borrowing.
The availability of a national library card remains a popular suggestion from library users and patrons year after year. However, neither ALA nor PLA (Public Library Association, a division of ALA) coordinates national public library service.
Due to the process by which public libraries are funded, the establishment of any national reciprocal borrowing privileges is a bit more complex than you might imagine. Public libraries in the U.S. are set up under a local governance model, as the majority of funding for most public libraries comes from local taxes. On average, nationwide, local taxes are responsible for over 80% of public library funds, with 10% coming from state sources; federal interests contribute less than 1%.
Also, there is no mechanism set up by which the materials borrowed by “national” library users and patrons could be returned to their home institutions—which are presumably a state or more away--in a timely manner. Nor is there a mechanism to ensure that these materials would be returned. Creating such a multi-state secure mechanism that would protect and secure the varied collections of all of the libraries across the country from any misuse or abuse of a national borrowing system would pose a formidable challenge.