What is this community?
It's a place for people to post recommendations of books, movies, television series, graphic novels, etc. featuring queer and/or genderqueer protagonists with happy endings. Despite the word "gay" in the community name, those protagonists by no means have to be restricted to gay men; I just liked the pun. Anything with gay, lesbian, bisexual, asexual, transgender, or intersex protagonists works.
Who exactly is a protagonist?
Ideally, it'll be the main character(s). Most people aren't going to be interested in reading 350 pages or watching a twelve hour miniseries just because there's one scene where the main character gets her hair cut, and the male hairdresser's boyfriend brings him a bagged lunch. They might be totally happy and sweet together, but that's still only a few minutes out of a long narrative.
On the other hand, if there are secondary queer characters whose story constitutes a significant subplot, that's okay. Use your best judgment.
What constitutes a "happy ending"?
This is obviously a matter of interpretation, as well as one that looks a little different based on the medium. Stories about dying of AIDS, being killed by gaybashers, turning straight, being dumped because one's partner discovers the protagonist's gender assignment at birth, or being dumped because one's partner turns straight are obviously ineligible. Stories where the protagonists are unwillingly outed, break up for non-straight conversion related and non-transphobic reasons, or have to stay in the closet for the whole story might not be eligible. Few narratives are going to have Disney perfect endings, but don't recommend anything where the angst outweighs the happy, fuzzy vibes.
Tackling the subject of the medium: if a book or a movie has a happy ending for its queer protagonists, it's eligible even if a sequel later breaks them up, kills off one of them, etc. A miniseries, manga series, or similar multipart narrative needs to have a happy final episode or volume. Television series and long-running graphic novels (e.g. The X-Men)...are a little more complicated. For now, let's say that a series with closed canon needs to have a happy final episode or volume. If a series is still running, you ought to note that in your recommendation, and should one of the queer protagonists die or turn evil or turn straight or whatever, please edit your entry with a non-spoilery note saying that the series becomes more problematic in its depiction of queerness later.
Is it okay to recommend fanfiction?
Given that fanfiction is one of the few media where finding stories with happy endings for queer protagonists is immeasurably easier than finding stories with unhappy endings for queer protagonists: no, sorry.
Do happy endings require romance?
Not necessarily. Say you have a book about a lesbian spy that's focused on a particular assignment she's been given. Her lesbianism is an important part of her characterization--maybe it affects her relationship with her primarily male targets, or maybe she has a couple of one-night stands over the course of the story--and there's little to no angst about the fact that she doesn't have a longterm partner. In that context, a happy ending would be the spy completing her mission safely.
Just be careful that the protagonist's queerness really is integral to the story and that the angst about being single and/or queer is kept to a minimum.
Behind a cut-tag, please, with warnings above the cut. If you're going to discuss spoilers in the comments to someone else's post, give fair warning there, too.
If you could tag your own posts, that would be awesome. Recommendations should be tagged by author, artist, director, or editor (a:[name], i:[name], d:[name], and ed:[name], respectively; names should be written family name first, given name second); genre (g:[genre]; e.g. mystery, sf/fantasy, etc.); medium (m:[medium]; e.g. film, play, book, manga, etc.); and variety of queerness(es) represented in the work (q:[type of queerness]; e.g. gay, lesbian, transgender, etc.).