LGBTQ is an initialism (an abbreviation made from initials) created to give a name to various sexual orientation and gender variant groups.

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. Going from “gay” to “gay and lesbian” to “gay, lesbian, and bisexual,” then “gay, lesbian, bisexual, and transgender” (LGBT), more letters have been added over the years, along with the original four:
G – Gay
L – Lesbian
B – Bisexual
T – Transgendered or Transsexual or Transvestite
Q – Queer or Questioning
U – Unsure or Union
I – Intersex
A – Allies or Asexual
P – Pansexual or Polyamorous
2S – Two-Spirit
O – Omnisexual or Other
There is no consensus of what the initials should be. The effort to apply a blanket name to the entire community of Gay-related groups has proven difficult. For much of history, many names applied to Gay people have been in-group code, inaccurate, overly medical, politically charged, and pejorative. Using the acronym also suggests compartmentalizing various groups apart from each other without recognizing that people may belong to more than one category.

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, 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 has created its own controversy. Early applications of this process included both GLB and LGB. People are not in total agreement whether the order should begin with a gender-neutral term (Gay) that has not always been gender-neutral, or with a group that faces double discrimination (sex and orientation) be given the place of honor (Lesbian). Because the history of Gay Liberation includes marginalization of women, LGB has gained currency of GLB in most forms of the acronym.

etsy.com/listing/82852526/tlgb-translesbiangaybi-pin-125-from, April 2012
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
That some disparate groups identify using the same letter can lead to confusion and offense. Transgendered, Transsexual and Transvestite are closely related, though not synonymous. “Questioning” is sometimes represented as distinct from Queer by use of a question mark, in the process causing grammatical confusion (“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, GLBT, and LGBTQ are the most commonly used variations (perhaps for their brevity), however other variants can be found, particularly among organizations. This list includes GLBTA (University of Iowa), LGBTQA (University of Vermont), LGBTQI (University of California-San Diego), and LGBTTIQQ2S (Toronto Pride) in the year 2010. But LGBTTTQ?UIASAP2SOOU has yet to catch on.
– Bowen Riley
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.