Favorite of all-time might have to go to Xandir from Drawn Together (see: my avatar). His character helped me a lot with my own coming-to-terms and coming out. Other characters: Justin from Queer as Folk - Mostly because he's adorable, and has a very interesting character arc throughout the show. A genuinely likable character who just seems to have his life against him, yet he always gets back up. Sam from Gone Home. Again, this game was the right place, right time for myself. I felt such a deep connection to her story, and she was written in a way that felt real. I felt like I knew her. Her voice actress did an amazing job selling her story. Thomas from Downton Abbey - Even though I wouldn't say I necessarily "like" him, I always find myself routing for him. He's written with real flaws, and you can tell the world has made him bitter, but he always has a heart. Plus, whenever something happens where he could be gay and happy but has to repress it, you can't help but feel for his character.
Lexa from The 100. I rarely watch movies and TV shows anymore because they usually end up disappointing me and I can't really get into TV shows that don't have any lesbian characters. Oh well. I still have video games and fanfiction.
The Wandering Son (an anime) probably has the best (mainly trans) representation I've ever seen in mainstream entertainment. However, fanfiction is still my personal go-to place for good LGBT representation.
Connor from HTGAWM. I like how there's a no nonsense attitude towards his sexuality and isn't a contributing factor to his personality, except when he's shown actually being 'gay'. No spoilers please I haven't started S2 yet. I also like how Aaron is portrayed in Emmerdale, too, but I won't say anything about that.
Willow and Tara from Buffy. Neither character was crazy (except at the end of season 6 but can you blame her?) or promiscuous. Their relationship was probably one of the most healthiest on the show, or on any show. I like that they were shown as just a happy couple in love, and the fact that they were both women wasn't an issue.
I loved Queer as Folk. I really hoped to see Brian and Justin get married in the end. I loved the whole scene in the house Brian bought for them and him explaining to Justin how he is now fervently committed to him. So sweet.
I loved Brian and Justin from Queer as Folk because they were really sweet. I am still not done watching this show and I can't wait to have some free time to actually do it. Bo and Lauren from Lost Girl, although Bo kind of annoyed me because she went back and forth whatshisface werewolf guy (I am terrible with names to be honest). The guy was ok, and I know why Bo left him in the first place, but it still got on my nerves. I mean I get that Bo swings both sides but I kind of don't like how they painted her character. Not all bi people go back and forth people. :/ Lauren was badass though. Hands down. And Vex. I have no idea what exact sexuality he has, but I love his character. He is an asshole, true, but the kind that kind of grows on you. Also, there's Captain Jack Harkness, our awesome omnisexual man from Doctor Who. He is just adorable. And the inter-species lesbian couple from D.W. just rocks. Those chicks know how to solve a crime!
Not really watching shows specifically because they have an lgbt character. But if I had to go with one it would be David from Six Feet Under. Apart from being very real and not stereotypical, it was more than 10 years ago too.
Korra from Legend of Korra. I know it's never been mentioned in the show that she's bisexual or she's dating Asami, but it's pretty obvious and the creators even said that she was. I think she's awesome in so many ways, and well developed. She's strong. It's not forced down your throat that she's dating another woman, in fact, it's not even mentioned. She didn't leave Mako for another girl, or cheat on him for another girl (yes, she cheated on Mako, but that was for a boy, so I'm not really counting that). She doesn't crush on everyone she sees. Plus the fact that there's a bisexual in a family show?! It's rare for a bisexual to be in any show!
All in the Family, an older sitcom, had a lot of great portrayals. Not only with sexuality, but gender, race, and religion, as well as social politics. I don't know if something like that could fly nowadays.
Someone's never seen Till Death Do Us Part, the British series it was based on! The archaic attitude of Alfred Garnett was meant to be satirical, but unfortunately lots of people didn't understand that racist, sexist and homophobic attitudes were being mocked. But, yes, All In The Family was good for portrayals, just not its predecessor.