I'm fairly sure in Temple of Elemental Evil, there was an openly Gay Pirate character who any male members of your party could marry.
He was kind of comedic though, and slightly insulting from what i remember, its been years!
I'm surprised this hasn't come up before, but it is interesting to note the range of LGBT characters in games; those that are good, and those that are purely for mockery or titilation.
Examples I can think of offhand in rough categories:
THE GOOD-
Jade Empire- Romantic subplot available between player character and Silk Fox and Sky if female and Silk Fox and Dawn Star if male. Silk Fox and Dawn Star are female, Sky is male.
Mass Effect- Romantic subplot available between player character and Liara T'Soni, for both male and female players. (Liara is an Asari, an alien race who appear to be female, but are 'nongendered' I could probably write an essay on why I don't believe that to be true, but I'll save that one)
Knight of the Old Republic- Slight romantic subplot available between female player character and Juhani, who it is also implied was in a relationship with another female Jedi.
The Last Express- Two of the female passengers on the train spend pretty much all their time together, and if you read their diaries it is heavily implied they are lesbians. They hold hands a lot too, heh.
The Longest Journey- Fiona, the landlady of the main character, is a lesbian, and lives with her partner Mickey, although it was partially a device to show how society was going downhill, they were perceived as normal. The dialogue with Fiona was often somewhat crude, but utterly hilarious.
Metal Gear Solid 2+3- One of the villains, Vamp, is bisexual and had relationships with fairly prominent characters of both sex and no-one batted an eyelid. Similarly in the third game, another Villain was shown to be bisexual, having lovers of both sex.
Fable 1+2- In the first game you could only play as male, but options for romancing other men was present, and you could be either heterosexual, bisexual or homosexual. Fable 2 expanded on relationships, and allowed gay marriage and to play as a female character. There is also a quest to find a boyfriend for a farmer's son.
The Sims- Gay marriage!
THE BAD-
Mario- The character Birdo (You know the pink thing that spits eggs) in one of the original manuals, is identified as male, but wants to be female and called 'Birdette', this was pretty much censored and glossed over. Birdo is now female.
Fear Effect 2: Retro Helix- Two characters were purportedly lesbians, but it was blatant male titillation and heavily advertised in the media.
Final Fantasy VII- Cloud in a dress, need I say more?
Star Trek Voyager: Elite Force- Don't get me wrong, I love this game as a Voyager fan (particularly as you can explore the ship) you can choose for the player character to be either male or female, and a female crewmate will flirt with you regardless of sex. In the sequel, the choice of sex was removed forcing a heterosexual relationship.
Final Fight- The characters of Poison and Roxy were transvestites, but were censored to have less revealing clothing, and no mention of their real sex.
Enchanted Arms- Makoto is a bad stereotype of an overly flamboyant gay man, who identifies as a lady, generally not well accepted as he is just a really silly character.
I could probably think of more examples but it's late and I'm out of steam. Discuss and add people!
I'm fairly sure in Temple of Elemental Evil, there was an openly Gay Pirate character who any male members of your party could marry.
He was kind of comedic though, and slightly insulting from what i remember, its been years!
I'm pretty sure Neo Cortex in Crash Bandicoot is gay, he has gotten really camp, if you have played any of the newer games specifically Crash of the titans quote:
Video:From IMDB:
Doctor Neo Cortex: [through a megaphone] Is... is this thing on? Yeah? Ha ha! I'm back, babies! Surrender to Cortex!
Crunch Bandicoot: Make us, sucka!
Doctor Neo Cortex: Hey, genius. I can't actually hear you. I'm really far away and I'm flying like a hovercraft or something.
http://www.youtube.com/watch?v=swwynzTGk4A