LGBTQ is an initialism (an abbreviation made from initials) created to give a name to people with atypical sexual orientation, gender expression, or sexual physiology.

campushealthmedia.arizona.edu/mental.htm, April 2012. Top image: uasasonoma.org/teensite/home_lgbtq.html, April 2012
Origins: The Challenge of Naming
The LGBTQ initialism was created in an effort to be as inclusive as possible without recklessly collapsing distinct identities under a single moniker. More letters have been added over the years, along with the original four:
G – Gay
L – Lesbian
B – Bisexual
T – Transgendered or Trans,
then
Q – Queer or Questioning
U – Unsure or Union
I – Intersex
A – Allies or Asexual
P – Pansexual or Polyamorous
2S (TS) – Two-Spirit
O – Omnisexual or Other
The effort to apply a blanket name to the entire community of Gay-related groups has been rich ground for innovation, and there is no consensus of what the initials should be. Using the acronym suggests compartmentalizing various groups apart from each other without recognizing that people may identify with more than one category, or with none of them.

From University of Missouri-Kansas City’s LGBTQI website (umkc.edu/lgbt/LGBTQIA/Home_Blog/Home_Blog.html, April 2012)
The potential for the initialism to become unwieldy has been an issue for the community. In Gay folk speech, one of the names for the acronym has been alphabet soup, referring to an almost indecipherable mass of seemingly random letters that is not understood outside of a few politically correct activists. As such, the acronym may do the opposite of what it was designed to do: its opaqueness may render the entire collective invisible.
Sequence
The sequence of the letters created its own controversy. People are not in total agreement whether the order should begin with a gender-neutral term (Gay) that has not always been gender-neutral (after Stonewall, “gay” became equivalent to “gay male”), or with Lesbian, a group that faces double discrimination of sex and orientation. Because the history of Gay Liberation includes marginalizing women and putting women in a lesser category, L comes before G in most forms of the acronym.
Some groups place “Gay” further down the sequence in favor of other identities. That practice is usually a sign that those groups identify “Gay” with “born male,” and are striving to minimize patriarchal discourse and heteronormal dichotomies within the community.
Letters of Reference
Some disparate groups identify using the same letter. “Transgendered,” “transsexual,” and “transvestite” are interrelated terms, though not synonymous – nevertheless, the term Trans has been used to represent all three. “Questioning” is sometimes represented as distinct from “Queer” by use of a question mark, in the process causing confusion for the reader (“I just donated to the local LGBTQ? civil rights organization.”). Straight Allies are sometimes referenced with an S followed by an A, but that could cause confusion if the A is taken to mean “Asexual.” The all-inclusive O for Other creates the most ironic of problems for an effort to include as many people as possible. Although O has been used for those who are isolated and alienated for being different, it also resembles a nameless “miscellaneous” category. In addition, “other” is often used in reference to detrimental marginalizing, as in a group being “Othered.”

A playful take on the LGBT acronym: “OKay To (2) Be Me” (ok2bme.ca/content/glossary-symbols, April 2012)
Common Usage
LGBT and LGBTQ are the most commonly used variations (perhaps for their brevity), however other variants can be found, particularly among organizations. In 2010, this list included GLBTA (University of Iowa), LGBTQA (University of Vermont), LGBTQI (University of California-San Diego), and LGBTTIQQ2S (Toronto Pride). LGBTTTQ?UIASAP2SOOU has yet to catch on anywhere.
– Bowen Riley and Mickey Weems
QEGF Authors and Articles
QEGF Introduction
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Further reading:
National Gay and Lesbian Journalists Association Stylebook. http://www.nlgja.org/resources/stylebook.html, accessed July 2010.
GLBT Student Pride Network Directory of Campus Organizations. http://www.glbtstudentpride.com/United%20States%20Colleges/unitedstates.htm, accessed July 2010.
LGBTQIA Glossary – UC Davis LGBT Student Resource Center. http://lgbtcenter.ucdavis.edu/lgbt-education/lgbtqia-glossary, accessed July 2010.