If you feel your month is not represented in this list, which is not intended to be exhaustive, then post a comment. Clearly, we have a lot to celebrate as librarians.
With some regret, we could not find a Library Vendors' Month. Perhaps that month exists, and we simply could not find it at the top of the search results.
Has anyone created a calendar with every library month, week, and day on it?
FEBRUARY
Library Lovers' Month [Friends & Foundations of California Libraries]
There are several public libraries that seem to have a "library month in February."
APRIL
National Library Week [ALA]
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School Library Media Month
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April 13
National Library Workers Day [ALA-APA]
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April 14
National Bookmobile Day
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Banned Books Week [ALA's Office for Intellectual Freedom]
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April 15
Teen Literature Day [YALSA]
SEPTEMBER
Library Card Sign-Up Month [ALA]
September 8
International Literacy Day [UNESCO]
OCTOBER
Canadian Library Month
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International School Library Month
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National Medical Librarians Month
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Fourth Monday in October
National School Library Day [e.g. British Columbia Teacher-Librarians'Association]
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Theological Libraries Month [American Theological Library Association]
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National Information Literacy Awareness Month
There are many, many more library months, weeks, and days to celebrate.