Type in "Batman and Robin" to google images. On the first line of pictures there will be a picture of the two making out. That says it all really.
Lord knows where they got it from but many people interpret Batman as having plenty of Ho Yay. One Moral Guardian, Frederic Wertham, famously claimed that it was "homosexual propaganda". Some later writers intentionally joked around with this.
Among other things, Joker is occasionally thought to have feelings for Batman that go beyond simple obsession and into romantic obsession. In one scene, he tortures Lex Luthor, and Lex Luthor asks him if he is upset that Batman loves Catwoman more than him. Joker looks almost adorably bewildered for a moment before flying into a rage and jacking up the torture level.
"Joker, does it ever bother you... really bother you... that Batman will always like Catwoman better? Blow up his city all you want, he'll never take you to the prom!"
Subverted in a Batman Confidential, when Batman commits a crime as his criminal persona, Matches Malone, so he'll get sent to jail, get put in the cell next to Joker's, and pick his brains. After Joker recognizes him-in about five seconds-Batman changes clothes right there, causing Joker to turn around and cover his eyes. "Don't worry. I like-a the ladies."
More or less confirmed in the Cacophony mini-series where Joker's stated dreams are to humiliate Batman, kill him, then violate his corpse sexually. (What? You were expecting something ROMANTIC or even sane from the Joker?)
The Bat and the Cat storyline from Batman Confidential. Long story short, Batgirl and Catwoman chase each other all over Gotham for possession of an important notebook. And at one point, this◊ happens. It certainly does look like angry sex.
Two throw-away characters in a Harley and Ivy comic (based on the animated series) are depicted as being gay themselves as a sort of joke, a pair of lumberjacks called Slash and Burn (Slash has chainsaws, Burn has a flamethrower). When they try to bring in Harley and Ivy, the two try to get them to let them go free by asking if they would do it for a pair of cute girls like themselves. The two just look at each other knowingly before jumping into combat.
Reputedly, this (plus the spandex-clad TV series) is how the name "Bruce" became associated with homosexuality. Of course, his original ward's name is suggestive enough on its own.
The Joker makes a couple of Ho Yay jokes about Robin in Grant Morrison's Arkham Asylum. After the Joker greets Batman with a slap on the buttocks (throwing him into a rage), he asks, "How is the Boy Wonder? Started shaving yet?" Later, when Batman claims to see nothing in an Inkblot Test card, the Joker says, "Not even a cute little long-legged boy in swim trunks?"
Not to mention in a very similar case of taking over the asylum and having fun with The Creeper, Joker mentions to him "That laugh of yours... It just makes me tingle all over"
In the first issue of Harley Quinn's solo series, a theme park is opened, with versions of Batman and Robin. Robin is cast as a curvaceous, pretty young woman, which the producer explains that:
Producer: I know some stories say that the kid's a guy—but in a costume like that? C'mon—this is family entertainment!
Batman refers to Robin as being his "partner", and didn't stop even when "partner" took on the meaning of "lover".
The relationship between Batman and his Robins is explicitly stated as being not quite father-and-son. Dick's affection for Bruce, in particular, is canonically judged by other characters as being, well, a little too much.
During the Hugo Strange arc in Batman: Gotham Knights, Hugo psycho analyses Dick's feelings for Batman as being sexual in nature
To be fair, that arc was written by Devin Grayson, who has long held the view that Dick has a deep rooted sexual attraction to Bruce Wayne, his father figure who is not actually his father.
Also, during this arc, Strange is depicted as extremely, y'know, crazy.
Not to mention that the second Robin (who was the first child to be adopted by Bruce, years before even Dick), Jason Todd, went on a Roaring Rampage of Revenge after he came Back from the Dead that was mostly motivated by his finding out that Bruce hadn't broken his one rule to avenge Jason's death.
Jason: And doing it because... ...because he took me away from you.
Though that's more likely due to Jason seeing Bruce as a father more than anything else.
Though the "I just love to watch you work" scene says otherwise.
Taken to truly ridiculous levels in the Superman Batman comic series written by Jeph Loeb (oh, and as if that title wasn't putting it in neon lights either), in which pretty much every thought-caption that Superman and Batman had about each other was describing the other in the most ludicrously fawning tones about how the other really was the best hero ever, to the point where it really wasn't funny any more.
Amendment: not funny any more when Jeph Loeb himself does it.
The thing is, Loeb was by no means the first writer to make you doubt the heterosexuality of Superman and Batman. I would dare say that honour goes to Doug Moench in ''World's Finest'' #289, also covered here. It starts off with the two seeking comfort in each other at the Fortress of Solitude one lonely night and Holy Mother of God, does it go downhill from there (or uphill, depending on your point of view). It ends with - swear to God - Naughty Tentacles, and the two of them embracing. And with dialogue like this (emphasis so not mine):
Superman: We're like night and day, you and I, and yet we're closer than we realize, closer than twins because we complement each other... we fit each other... like a hand and glove.
Narrator: They hold the grip for a long time....
As a commenter said, "I think the only way this would be less subtle without actual porn is if it ended with a tasteful shot of them snuggling in bed together."
There was an Elseworld comic in which Kal-El's rocket landed in medieval Japan, and the medieval Japanese equivalent of Batman was a woman. The results were...predictable.
Further referenced in their animatedseries crossover, when Bruce Wayne's obvious interest in Superman leads to Lois asking "You want me to fix you two up?"
Maybe it's just something about Batman— there are even some moments of Ho Yay between him and Jim Gordon. Such as the scene from Batman: No Man's Land. Tim's right: it does feel like your parents are fighting. Bonus points when you consider Babs has two dads.
Batman does have a history of sneaking into the bedrooms of attractive, naked young men. See his relationship with Green LanternKyle Rayner, when he did so to assure Kyle that the League thought of him as the true Green Lantern. Kyle was a bit of a Batman fanboy, as well.
Even Alfred has his moments. In All-Star Batman & Robin, the Boy Wonder, there's a scene where, thinking to himself, he describes Batman as his "black-eyed, brilliant, willful angel". As if Batman's interactions with Robin weren't Squicky enough...
Catwoman and Talia's scene in "Hush", with Talia tied up in Catwoman's apartment with Catwoman casually circling around her, kind of gives off these vibes.
There's also the flashback of the two together toward the start of the "Gotham City Sirens" series.
They actually had some of this pre-Crisis as well.
The biggest amount of Ho Yay came from the aftermath of Infinite Crisis, which Tim obsessing over trying to create another Con. There was also him dating Conner's girlfriend Wonder Girl, which was riddled with problems and came off as creepy.