Gay Option

Mass Effect 1 and 2 has romance options for a mono-gender race with feminine appearance called the Asari. Mass Effect 3 has gay and lesbian romance interests. Kaiden Alenko is bisexual and romance-able by a male Shepard.

Lloyd can choose a male or female soulmate. Zelos, the character on the right, says

Put on a show that will make me fall in love.

In one skit, Zelos calls Lloyd hunny (in my playthrough this happened once Zelos was Lloyd's soul mate). In another Zelos tells Loyd

...Heh heh. Those are such cajoling words... If you want to think that way, then that's fine.

Fallout 2 has gay and lesbian marriage. Fallout 3 has a bisexual female prostitute, but prostitution is a minor part of the game. Fallout: New Vegas has one gay and one lesbian companion (non-romantic) character; you can use the confirmed bachelor perk on Arcade Gannon and other characters.

The prostitution is very underwhelming. Your character pays for it just like anything else and nothing is shown.

Characters aren't romanceable in Fallout 3 or New Vegas.

Jade Empire has a romance option (wikia) for Sky and Silk Fox; for the Sky romance, you need to be extra careful not to be locked out.
Unfortunately, studio heads decided to censor and blackout the gay kissing scene. This mod restores the scene.

Marriage: Fable I is an excellent game. The atmosphere of the second game isn't as excellent, but there are many game-play improvements; unfortunately, the second game simplifies the game-play when it isn't needed (e.g. far less spells). Fable III reviewers say the plot isn't as good and the game-play is too simplified.
Fable TLC is available on PC, but the mods are limited. To my knowledge, Fable II and III software prevents mods from being made.

Marriage: The Elder Scrolls V has marriage unlike Morrowind and Oblivion.

A short marriage guide is on IGN and a more detailed guide is on Elder Scrolls Wikia.
Every romance-able character is bisexual.

Dragon Age I has a male and female bisexual character, but you can install a mod to make Alistair and Morrigan romance-able.

The 2nd Dragon Age is criticized for similar dungeons and EA's choice to rush the release. Every romance-able character is bisexual in the second game.

Juhani's romance subplot is the only same sex romance option. I read it's possible to switch your gender for KOTOR with a save game editor, but Carth will call you a woman.

It's up to the player to decide if they think Ike and Soren are more than just friends.
To be able to get the converseration in Radiant Dawn, you need to transfer a save where Ike and Soren have A support, get A support in POR, and recruit Lehran which can only happen on a second playthrough.

Façade is an interactive story that enters the uncanny valley and can be hilarious, but it's an interesting benchmark in interactive gaming. You can flirt with either character.

Dys4ia is a poignant short autobiography about a trans-woman.

These games aren't pornographic.

Persona 2 Innocent Sin was released in Japan only and is available on PSP; fans made an English mod for the original PSX version. Persona is a spin-off series of the Megami Tensei series.
One of Persona 4's playable characters (not the main character) comes to term's with possibly being gay or biesxual; the Atlus interview has minor spoilers.

A few characters are romance-able if you mod the game.
Nathaniel - gay mod
Arath - bisexual mod
Faren - bisexual mod
Solaufein - bisexual mod
There are also lesbian mods. More mods are posted on this forum page.

Fear Effect 2 is a prequel to Fear Effect. In an interview one of the designers of Fear Effect 2 said

Once and for all, let me set the record straight. Hana is not a lesbian! She likes men...and she likes women. Who she chooses to go to bed with at the end of the day is not a big deal![...]The only reason I wanted Hana to have a female companion this time around is because it gives me the ability to create an extremely interesting love triangle further down the road.

The main character can kiss boys as well as girls.

This is an RPG aimed to combat homophobia.