The Joker of Batman fame. Since Harley's transition from the DCAU into canon comics, the writers have been seemingly trying to tear them apart and made it into a one-sided relationship on her part. Harley & Ivy both think that The Joker only has eyes for Batman. Joker has often professed affection towards Batman (complete with moments of desperate attention-needing) and has made some awkward comments about Robin's shorts and shaving habits. He seems to have quite a flirtatious love/hate thing for Lex Luthor as well. The Joker is also very keen on his appearance and once said he didn't want to see Batman until his nails were finished drying. He also took off his pants in front of Onomatopoeia and told him that he "bottoms from the top". As counter-evidence, The Killing Joke showed the not-yet Joker's pregnant wife saying that he was "good in bed", but the entire segment falls into his Multiple Choice Past. In Arkham Asylum: A Serious House on Serious Earth Joker slaps Batman on the butt and continually hits on him throughout the comic. The pages are lined with homoerotic content and an unnatural level of sexual tension. (Arkham is non-canon, though its status as one of the iconic Joker portrayals means it can't be discounted because of that.)
Various Batman media have run with this. Batman (1989) shows that Jack Napier, the man who became the Joker, had more than a casual interest in art and was very keen on his appearance. In The Dark Knight, the Joker disguises himself as a white-skirted nurse to blow up a hospital and, in his last meeting with Batman, looks forward to many future encounters with him and tells him: "You complete me." Batman: Mask of the Phantasm has him bat his eyelashes when he sees his old mob boss for the first time in years.
Batman himself borders on Ambiguously Gay or Bi at times. Some writers make the Batman/Joker Foe Yay go both ways (as if it wasn't disturbing enough) and portray Batman as having some bizarre obsession with the Joker. Frank Miller actually writes Batman as being gay but simply sublimating his sexual urges into crime fighting, which caused Miller to joke "He'd be a lot healthier if he was gay".
The Creeper. With DC Comics' original run, this was probably unintentional, but it's difficult to believe that it was. The title character appears to be wearing nothing but boots, gloves, briefs, and a feather boa, reveals himself (briefly) to be a masochist, and likes to shock his enemies with his flamboyant mannerisms. Somewhat less stereotypically, The Creeper's civilian persona, Jack Ryder, has a dislike bordering on hatred of female affection and immediately takes his male coworker up on his offer to buy an apartment together.
His origin story explains his costume as being what he could drum up on short notice at a costume shop (all the good costumes were already rented, and what he got was a box of odds and ends) and his mannerisms as him realizing that the bad guys were freaked out by his appearance and deciding to just run with that. None of this is proof that Jack isn't gay, of course.
Gil Thorp: Lini Verde, a flashy-dressing Glee fan who's also a clinch player for the basketball team. Despite the large number of signs, his sexual orientation hasn't been stated. The storyline involves a website that calls him unpleasant names, but the exact nature of those names is unrevealed (probably a good idea for all sorts of reasons). When one character suggests wearing pink to support him, she gets the response "This is about bullying, not ... pinkness!"
It's Grim Up North London: Jez and Quin in the Private Eye comic strip. Maybe they're a stereotyped gay couple; maybe they're an equally stereotyped pair of upper-middle-class artistic types, who happen to share a flat.
In Secret Six, Catman and Deadshot are initially BFFs who other characters jokingly say are in love, but the final issue implies that they may legitimately be in love with one another. Word of God confirmed that Catman at least is bisexual, while Deadshot's not so certain.
The Marvel Comics supervillain Man-Killer from Thunderbolts was... actually not that ambiguous, but the comics spent years not actually stating it directly. Aside from her name, her stereotypically butch appearance, and her firm rejection of any men who showed any interest in her, there's this little exchange from when she decided to try being a good guy.
Cyclone: One more goes to the other side... Man-Killer: I was born on that side, Frenchie. Cyclone: I meant — oh, never mind.
Adrian Veidt, of course. The movie version fits the trope fairly well, the book a bit less so.
Rorschach: He is pampered and decadent, betraying even his own shallow, liberal affectations. Possibly homosexual? Must remember to investigate further.
Rorschach: The "holding a handshake too long" scene that demonstrates Nite Owl II's sexual tension for Silk Spectre II is mirrored later with confirmed bachelor Rorschach doing the exact same thing to Nite Owl II. Plus he has mommy-issues and possibly idolizes his dad.
Post-crisis, it is revealed that most residents of Themyscira are the immortal reincarnations of women who were wronged or abused by men and are all (mostly) misandric as a result, giving them a Freudian Excuse for avoiding men.
The title character of Yoko Tsuno never appears to have a boyfriend, but she eagerly bonds with cute young women throughout the series, which makes quite a few fans wonder about her sexual orientation. In later albums the author tries to couple her with her best friend Vic, even though they don't even have a fraction of the chemistry Yoko has with some of the other girls — especially Ingrid.
Cacofonix from Astérix. He is the only male villager to have neither a wife nor occasional love interests, he plays up to stereotypes of camp, self-declared artists, and in Asterix and the Secret Weapon, while living in the forest with the rest of the village men in an all-male society, there are love letters pinned to his tree.