A fanzine library is a term applied to both formal and informal collections of fanzines that can be borrowed and read by fans. They are often referred to as "Lending Libraries" and are very much similar to Fanzine Reading Rooms which operate at many conventions.
Unlike convention Fanzine Reading Rooms, where the zines must be read and consumed on the premises, Fanzine Libraries often allow fans to check out fanzines and take them home for an extended period of time. Academic fanzine libraries maintained by Universities generally operate as Special Collection Libraries and restrict both physical and circulating access.
One unique library was the The Fanzine-Taping Service for Blind and Print Handicapped Readers, a fan-run service for those fans who were challenged by tradition print fanworks.
Early History of Fanzine Libraries
As soon as Star Trek fanzines proliferated, fans were calling for lending libraries. Early fanzines were expensive and print runs were limited, putting many fans into the awkward position of seeking out photocopied fanzines and being accused of zine piracy.
In 1973, Sharon Ferraro proposed a Star Trek Fan Literature Archive called Memory Alpha. "The August issue [of A Piece of the Action] had a proposal by Sharon Ferraro for a Star Trek Fan Literature Archive called Memory Alpha. 'The goal of MA,' she said, 'is to collect, catalog, and microfilm as much of the fan-produced literature as we can get our hot little hands on.' She then proposed to put all issues on microfiche for posterity. In the October issue, Sharon announced that 'Memory Alpha, the ST fan literature archive...has been accepted by the National Air and Space Museum.' This archive was a fine concept, but I have no information about it after the mid-1970s. Perhaps somewhere in the Smithsonian one may find a stack of fanzines, dating from 1967-1974, gathering dust in a corner somewhere." 
By 1976 fans were still discussing the need for a lending library. One fan wrote a letter to the Halkan Council: ""Being a librarian makes me think of a ST fanzine library -- like Memory Alpha... I mentioned an idea of requesting permission and copies of out-of-print ST fanzines to reprint them so fen will not be forever deprived of these 'classics' of ST literature.... Maybe the editors of these marvelous zines and gracious authors would be so kind as to grant legal permission, loan copies of their zines, give advice, encouragement, etc. This would not detract from the value of the original edition, because there are always those who want the first editions anyhow...." 
Other Star Trek fans tried to bypass fanzines and fanzine publishers and asked writers to circulate their stories directly to the readers, much like the circuit libraries that existed in The Professionals fandom. In issue 48 of A Piece of the Action Susan LaLoge announced the creation of a circulating library for Star Trek stories: "Do you like to read (or write) Star trek stories? Here's an organization you've got to join. It's a circulating library, of sorts, and operated for fun, not profit, so everyone can afford it. The initial deposit is $1 for bookkeeping fee, and $2 Xerox deposit. (In case you lose a story, we can get it back into circulation without delay). Stories will come to you in turn from the person ahead of you on the list, and you will mail them to the next person. Simple, no? Writers of course get no cash reward, but if they care to type their address on the bottom of their story, will get all the advice they can stand from readers....Writers are requested to send two copies of their stories and KEEP A THIRD! (Don't learn this the hard way like I did)."
Still very little concrete action seems to have been taken although there were several more attempts to start up a lending library. In 1983 a fan announced in Datazine #26 that she was collecting "classic Trek zines, both PG and Adult, for a non-profit lending library. Condition is unimportant so long as the zine is legible; unbound copies are fine. Anyone willing to part with a copy or an authorized xerox of an O.O.P. zine, kindly contact me."
It remains unclear whether any of these attempts were successful or gained widespread circulation.
Enter Ming Wathne, the 1980s and the Fanzine Archives
It wasn't until the early 1980s that a successful lending library was launched. This base of this first library were the zines Lucasfilm had collected in his effort to control and observe fandom. When the official Star Wars fan club folded, these zines were turned over to the First Terran Enclave, who ran the library for a year. When that library folded, the zines were not circulated until March of 1990 when Ming Wathne took them over and created The Fanzine Archives: A Library for the Preservation & Circulation of Fan-created Material. Ming eventually began accepting non-Star Wars fanzines, and by 2008, the Archives maintained a circulating library of over 300 fanzines and a permanent collection of over 3,000 titles. In early 2009, the Open Doors committee of the Organization for Transformative Works helped to place the Fanzine Archives with the Special Collections Department of the University of Iowa Libraries as part of their Fan Culture Preservation Project.
1990s: Fandom Specific Libraries Spring Up
By the 1990s, fandom had sufficient interest and acceptance behind the idea of a fanzine library to allow the creation of several smaller fandom specific libraries:
- 1990 to 2006 - S&H Lending Library (gen and slash) for both gen and slash Starsky & Hutch zines, lending a total of 64 zines
- 1991 to present - Crystal Rose Lending Library for Beauty and the Beast gen and het zines, lending a total of 800 zines
- 1995 to ? - ATeam Lending Library, for The A-Team zines and resources such as DVDs, tapes, and TV scripts
- active in 1996, the STAG Postal Lending Library
- 1997 to present - The K/S Library for 300+ Star Trek slash fanzines and 100+ gen fanzines
- 1997 to 2000 - S&H Lending Library (gen fanzines) for gen Starsky & Hutch fanzines, lending approximately 44 zines.
Beginning in 1992: A Unique Library
The Fanzine-Taping Service for Blind and Print Handicapped Readers was a fan-run library started in 1992 for fans who had difficulties with reading traditional printed materials. Fans recorded fiction onto audio cassette tapes that were then sent out to other fans.
After getting permission from a zine publisher, fiction from that zine was then recorded by a fan onto an audio cassette. That audio cassette would then become part of a library from which would be used to make other tapes. These tapes would be sold at cost to fans who'd requested them. To help ensure that only eligible fans would use these tapes, they were recorded in such a way that they would sound like gibberish on normal cassette players, rather than the cassette players sight-impaired fans received from the government. Sighted fans recored the fiction on regular machines, and the Janice and Marcia re-mastered the tapes for the special machines.
2000s: The Creation of Academic Fanzine Libraries
Starting in the late 1990s and early to mid 2000s, universities began collecting fanzines and making them part of their Special Collections. Often these fan fiction fanzines are part of a larger collection focusing on popular culture. As such university 'fanzine libraries' are more like archives than lending/circulating libraries with access restrictions and limited or no circulation.
Examples of Academic Fanzine Libraries
- University of Iowa Fanzine Archives. The University began collecting general science fiction fanzines starting in 2004. In 2008, Sandy Herrold selected the University for her Blake's 7 fanzine collection. In 2009, the OTW helped Ming Wathne place her 3,000+ Fanzine Archives which makes up the bulk of the University's collection. Other fans have followed suit and an active donation program is currently underway.
- Bowling Green State University's Browne Popular Culture Library. BSGU began collecting a wide range of popular culture material in the late 1960s, ranging from posters, to buttons, collectibles, fanzines and more. While their catalog lists 5000 zines, the bulk are general science fiction or other types of fanzines. As of July 2011, the library contains approximately 97 slash zines, with around 300 gen fanzines.
- University of California Riverside's Fanzine Collection. This large science fiction fanzine collection contains several hundred thousand fanzines. Special Collection 320 houses approximately 1300 Star Trek K/S slash zines and printed stories.
- Susan Smith-Clark's Fanzine Collection at the National Library of Australia. In the late 1990s, Susan Smith-Clark donated a portion of her fanzine and convention program guide collection to the National Library of Australia. It currently holds 100 of her calendars, and other fan club related material.
- One National Gay and Lesbian Archive K/S Collection. ONE National Gay & Lesbian Archives houses the world's largest research library on Gay, Lesbian, Bisexual, and Transgendered heritage and concerns. Starting in 2007, they began listing 67 slash zines as part of their K/S fanzine Collection.
- Temple University's Enterprising Women Collection. Temple University hosts a number of fanzines related to Camille Bacon Smith's book Enterprising Women (the "Enterprising Women Collection"). They may also host a smaller Star Trek collection that focuses on Klingons (the "Sue Frank Klingon/Star Trek" collection). These collections are part of the larger Paskow Science Fiction Fanine Collection. The finding aid for the collections are not available online so their dates and contents remain unknown. However in 2007, a visitor to the Sue Frank Klingon/Star Trek collection describes "six linear feet...of fanzines and organizational newsletters. These were assembled by Dr. Frank from groups within and outside of the U.S. -- fan groups are to be found in Britain, New Zealand, and Italy, among other places. The titles include "Klingon Assault Group Force Recon," "The Pillage Voice," "Engage!," "Disruptor," and "Something Else." The newsletters reflect the range of Klingon-related activities afoot in the terran world. They contain drawings, photos, recipes, letters, poems, stories, technical information, and analyses of many aspects of Klingon language and culture." 
The Notable Exception: The Professionals Circuit Library - 1980s to the Present
While the Professionals fandom never had a fanzine lending library, from early on fans circulated fan fiction directly to one another. These stories became part of the The Professionals Circuit, which continues to operate today. Although the bulk of circuit stories never appeared in fanzines, many writers would release their fanzine-published stories to the 'circuit' after the stories had appeared in fanzines and had timed-out. On occasion, a fanzine publisher would take circuit stories and, with the author's permission, republish them in a fanzine format with better formatting, clearer typeface and additional copy-editing. This fluidity would cause some confusion as stories might end up on the 'circuit' by mistake or when stories that had been available on the circuit for years were declared suddenly 'unavailable' because they were now offered in fanzine format.
Given that most attempts at creating fanzine libraries failed in the 1970s, fandom's reaction to the concept remained purely theoretical for many years. However, with the establishment of Ming Wathne's Fanzine Archives, worries similar to the zine piracy debates presumably took place.  Direct records of these discussions are currently not available, but the fact that Ming chose to circulate only out of print copies lends some weight to this idea. While a few fanzine publishers kept their zines permanently in print, it would have been harder for the typical fanzine publisher to argue their 'sales' would be hurt by a lending library once their zines were no longer for sale. Later lending libraries followed suit and offered only out of print zines or zines donated directly by the zine publisher.  Still, Ming, presumably out of an abundance of caution, allowed fanzine publishers until 1993 to opt-out of allowing their out of print zines to circulate. After 1993, however, she decided that the costs of catering to zine publishers changing views on zine lending were too high and restricted the opt-out policy.
- University of Iowa reaction
Fanzine Library Loan and Access Policies
- Sources of zines - buy, donate
- Opt in/Opt out
- Lending Policies
- Charging Policies
- International issues
- Access restrictions for Special Collections
- From Boldly Writing, page 16 .
- Halkan Council issue #18.
- A Piece of the Action, issue #48.
- Datazine issue #26.
- See the M.Horvat's Science Fiction Fanzine Collection which contains over 15,000 science fiction fanzines
- Klingons at Temple, posted October 19, 2007 to the PACSCL Consortial Survey Initiative blog.
- For example, some publishers felt that sharing of zines would result in lower sales and would limit their cash flow.
- The worries that free access to fanzines led to zine piracy were raised in a series of letters in the early 1990s discussing fanzine sales at Revelcon. See the Open Letter to Fanzine Readers, Contributors, and Publishers by Candace Pulleine for more details. One of the results of these letters was Revelcon announcing that fanzines could not be removed from the Revelcon fanzine reading room. One wonders how the idea of loaned fanzines being sent - unsupervised - into homes where they could be copied freely was received.
- See S&H_Lending_Library_(gen_and_slash), S&H_Lending_Library_(Gen), The K/S Library etc.
- In 1993, Ming sent a notice to The Monthly which explained the reasons for this new policy: "Due to the expense of making circulation copies, withdrawing permission to circulate an out-of-print zine can no longer be honored once a circulation copy has been made. If you have given permission under the old regulations and wish to remove that permission, please contact me before April 30, 1993. If a copy has not been made, the old agreement is still good."