ex-gay: a term most commonly used to describe someone who no longer identifies as gay, lesbian or bisexual. S/he typically still experiences same-sex attractions but seeks to abstain from sexual relations with members of the same-sex. Some ex-gays have suggested using other terms including former homosexual or even heterosexual. 
ex-ex-gay: (also known as ex-gay survivor or for drinking purposes Dos Equis) someone who used to identify as ex-gay, but has since acknowledged that change was not possible or necessary.
ex-ex-ex-gay: someone who used to be ex-gay, came out gay or lesbian, and then for whatever reason decided to be ex-gay again. Sightings are rare.
XXX gay: well, we're not going to go there!
SSA: Same-sex attractions
reparative therapy/conversion therapy: (from Box Turtle Bulletin) Before 1973, homosexuality was listed by the American Psychiatric Association as a mental disease. Consequently there were many different therapies to try to “cure” gays and lesbians. Usually these therapies consisted of psychoanalysis (or “talk” therapy), but sometimes these attempted “cures” were far more severe. Today most practitioners are religiously affiliated, and their methods range from occasional psychological or group counseling to more intensive live-in therapy programs. Some use conventional secular methods, but most rely on a spiritual conversion of some sort. Many of these groups refer to their members as “ex-gays.”
sexual reorientation therapy: Yet another name for reparative/conversion therapy.
aversion therapy: (from Box Turtle Bulletin) “Aversion” therapy often included painful electric shock or apomorphine injections, which caused severe gut-retching nausea. In the end however, there were very few “cures,” and today aversion therapy has been abandoned for ethical reasons.
electroconvulsive therapy: A form of therapy used to treat depression that has been used unsuccessfuly to cure or curb homosexuality.
(from your dictionary.com) Administration of electric current to the brain through electrodes placed on the head in order to induce seizure activity in the brain, used in the treatment of certain mental disorders, especially severe depression. Also called electroshock, electroshock therapy.
ex-gay ministry/change ministry: (from GLOW) Christian ministries specializing in helping homosexually oriented persons change their sexual orientation or at least live as though their sexual orientation is changed. The usual expectation is that persons will become heterosexually oriented. (BXG note: or at least no longer identify as lesbian, gay or bisexual)
ex-gay movement: Started in the early 1970's, a movement that initially sought to help people who struggled with unwanted same-sex attractions, but through the years became more politicized and involved in speaking out against the civil rights of LGBT people. The majority of participants and leaders are white Evangelical Christian males.
Exodus: An Evangelical Christian ex-gay umbrella ministry and the largest ex-gay organization in the US.
Desert Streams: A ministry that furnishes ex-gay courses and programs for individual church use. Desert Streams ex-gay courses include "Living Waters" (full 30-week course), "CrossCurrent" (an introductory 8-week course) and "The River" ("Living Waters" program geared for young adults).
Living Waters: A 30-week course hosted and taught in individual churches. Lay leaders who have taken a one-week intensive training seminar from Desert Streams lead the group in worship, teaching, small groups, and "healing prayer."NARTH: The National Association for the Research and Treatment of Homosexuality
Evergreen: Church of Jesus Christ of Latter Day Saints (Mormon) ex-gay ministry
JONAH: Jews Offering New Alternatives to Homosexuality (Jewish ex-gay organization)
Courage (UK): Previously an ex-gay ministry in England, through the courageous soul-searching of its leadership and members, Courage is now a Christian organization that affirms LGBT people
Courage (USA): A Roman Catholic ex-gay ministry that advocates abstinence in accordance to the church's teachings. Chances are once the Roman Catholic Church's teachings change, so will Courage.