Prior to 1989, the Comics Code Authority banned any mention of homosexuality under the umbrella of "sexual abnormality" in comics published in the United States. Since then, comic books have slowly gained LGBT representation, usually with occasional side characters. Queer comic book characters were pretty much always in the periphery until the 2000s, never acting as a major protagonist and certainly not featured in a major title.
In contemporary comics, there is much more representation. While not perfect, there are tons of comic series with progressive, gay characters waiting to be discovered by the masses. The time of delineation between gay comics or queer comics and more "traditional" fare is coming to an end. If you need proof, just check out these amazing comic book characters!
Since Harley's solo title launch in 2011, and her pop culture takeover thanks to Suicide Squad's success (flaws aside), she's become one of the most identifiable characters in the DC Universe. This is mostly a good thing.
Unfortunately, she's still often recognized as "The Joker's Girlfriend," which takes away from any name she's built up for herself. That's not even mentioning that the Joker is a physically and emotionally abusive partner, and nobody should ever be with him. Harley's relationship with Poison Ivy, by comparison, is significantly healthier and, frankly, adorable.
Batwoman was one of the first, and remains to be among the few, queer comic book characters that headlines her own title published by DC. Kate Kane, dishonorably discharged from the military while Don't Ask, Don't Tell was still in effect, finds herself inspired by Batman to take up the vigilante mantle herself after an encounter with some unsavory people. Greg Rucka's Elegy is a gorgeous origin story for her character and definitely a title worth checking out.
Hulkling (Teddy Altman if you're into secret identities), is a shapeshifting Skrull prince who was taken to Earth for his own protection during the Kree-Skrull war. On Earth, he was raised by a single mother. Apart from that, we don't learn much about Teddy's youth in the pages of Young Avengers, where he's graced the team with his presence since its formation back in 2005. On the team, Teddy meets Wiccan (Billy Kaplan) and starts one of the best romances in comics.
Billy Kaplan, AKA Wiccan, is the son of Scarlet Witch and Vision who almost didn't exist. Way back in Avengers: West Coast #52, it's revealed that Wanda Maximoff was so desperate to have children, she unknowingly warped reality. She created her twin sons with two fragments of a shattered demon's soul, causing them to vanish when the demon reassembled itself.
Billy was adopted by the Kaplans, and was a victim of bullying in his youth because of his orientation. This led to a confrontation with another student, revealing his mutant powers. He becomes a member of the Young Avengers where he meets Teddy Altman, AKA Hulkling, AKA the love of his young life.