Mostly, we are talking about RPG's that I've noticed, however "alphabet soup" (earlier I saw someone start in with the LGBTQQIU...didn't even get started good by the way, and LGBT generally covers it all for simplicity's sake) has permeated gaming since the '80's with not one, but two transwomen still in gaming today, Birdo and Poison, which is kind of odd art imitating life, but if you know anything about Civil Rights around Sexuality and Gender Orientation, you probably know that, or well, you should, but we're not talking about rights...we're talking about topics.
So, right there, you have a beat'em up/fighter and a platformer with two LGBT characters who are found throughout both games. Since then though, LGBT characters have found their way into numerous games, but three companies have stood out as actually being able to do something good with it; Bioware (KotOR, Jade Empire, Mass Effect, and Dragon Age), Square Enix (Final Fantasy Series, mostly, though a few others), and Atlus (Shin Megami Tensei series, specifically, Persona 4).
I'm not big on spoilers, so I'm not really going to explain all of these, but if I slip into spoiler territory, here's your warning.
I think Knights of the Old Republic was the first of these I noticed (mostly because my RPG experiences beforehand were Pokemon and Zelda, and while Tingle is running around in Rosy Rupeeland, there's really not much in either of those). The character of Juhani is just a character. Nothing really different about her. She's quiet, she keeps to herself, she's had a turgid past, but she wants to do right in the world (I played as a Jedi and not Sith, so, yeah). As you get to know her though, especially when playing as a female, you learn pretty late in the game that the reason she joined the Jedi order, and the reason she let her emotions get the better of her with her master, was that she basically had a crush on a Jedi Knight off to war...a female one at that. It's implied that after the game, she went off with the other Jedi who is perpetually worried about her.
I'm gonna stay away from the Atlus games in general, just because I've only played through a few of them, and then only just the one time, and go into Squenix territory.
Squaresoft was an interesting company over its span as its own entity...and when talking about LGBT topics in gaming, they're flagship series is the easiest place to look. Even after the merger with Enix, the company has continued to include LGBT characters and situations in their stories. So, let's just run down the FF Games LGBT stuff, as it's one of the top series in gaming period.
FFIII - Arc...not much else to stay there, as nothing was ever touched on it, and it's mostly speculative, but yeah, even if he wasn't meant to be, he certainly comes off as such. Also, since Arc didn't really exist as his own character until the remake, this may should find its way deeper on this list, but oh well.
FFV - Princess Sarah in this one was quite a bit different than her previous incarnations (FFI, FFIII). In this version, his name is Faris Scherwiz. And that's just the beginning. Faris is a pirate captain, and for the first five hours of the game, that's all you know about him. Get a little deeper, you find out that he is a she, and not that as the game progresses, but that she's a Princess. Whether or not Faris is transgender is up to debate, as the game continually keeps pronouns about the character pretty neutral, and that at the end, she does run off to join her crew after becoming bored with the throne.
FFVII - Situation Cross Dressing, and we're leaving it at that...because, swarms of fangirls scare even me...and I'm one of them...just not for him. Oh, and the gym owner that helps him, definitely.
FFVIII - It's there, but more for humors sake than anything else, with a brief cameo by a trans NPC.
FFIX - Quina Quen and Vivi; the young black mage and his potential love interest, the genderless Qu, Quina raise a lot of questions about Androgyny and Pansexuality, so, yeah.
FFXIII - Fang and Vanille, if you haven't played it, I wouldn't blame you, but yeah...front and center.
So, LGBT Topics are there, maybe even more so than film (how many LGBT Topics do you see in film where it's not actually a gay film?). Would it be better if there were more...maybe...though, they are found fairly frequently in games today. The issue is more that, with all characters, regardless of age, race, sexuality, gender, gender identity, or religion, they still need to be fully fleshed out in a lot of ways across the board. Sadly, RPG's seem to be the only thing really trying to do that lately, but we do still see a few things here and there.