See Foe Yay page for slashy tension between rivals and enemies (Draco/Harry, etc.)
Word of God confirms that Dumbledore was canonically in love with friend-turned-genocidal-maniac Grindelwald, hence his reticence in defeating him, and his lack of romantic relationships in later life.
You name it, it's been done in some form (yes, that includes Hagrid/Dobby)
Remus Lupin and Sirius Black. And how.
In the third book, Remus is very quick to believe Sirius' innocence — even though the truth just transfers the responsibility for multiple murders and Lily and James' betrayal and subsequent deaths from one former friend to another, he abandons suspicion for Sirius almost immediately and hugs him instead.
Similarly, the controlled, stoic Remus is noticeably touchy on the subject of Sirius, and clearly doesn't want him to receive the Dementor's Kiss... which isn't so strange, until you compare his later willingness to hand Peter over to the Dementors, or straight-up murder him (in front of three children, no less) for the same crimes. Even with the Dementor's Kiss viewed as a fate worse than death, there's a dissonance here.
Twice in the Shrieking Shack scene they exchange the same words:
"I think so."
Remus looks at Sirius, a lot. In the fifth book we even get this:
Lupin's eyes were fixed on Sirius.
*39 lines later*
"Personally", said Lupin quietly, looking away from Sirius at last.
Sirius and Lupin are known to have lived together from the end of Goblet of Fire until the end of the Order of the Phoenix, and give Harry a shared Christmas present (generally something done by couples). (Of course, both instances may be for practical purposes.)
Lupin only got with Tonks after Sirus died, and the pair are barely seen interacting, let alone developing a relationship.
One example: towards the beginning of the film version of Order of the Phoenix, in the first scene in 12 Grimmauld Place, there's a shot where Sirius just so happens to be sitting in front of a map, which Lupin just so happens to be reading over the top of Sirius's head. The result is a little like spooning.
Harry and Ron. Their fight in the Goblet of Fire resembled a lovers spat.
Goblet of Fire also gave us the chapter where the Triwizard contestants had to rescue "the thing they would miss the most" from the bottom of the lake. For Harry? It's Ron. Complete with Dobby going all Shipper on Deck by demanding Harry rescue "his Wheezy." (Although Fleur's sister had also been taken, which could suggest that Harry and Ron were close as brothers.)
It was even more explicit in the Malay translation of Goblet of Fire, where it was translated as "the contestants have to rescue the thing they love the most".
Harry asking Ron to go away with him before the wedding in TDH part one.
Later on, Ron pulling a shirtless Harry from the lake before their Crowing Moment of Heartwarming.
Ron helps Harry get dressed after he breaks his arm in Chamber of Secrets. Granted, they're twelve.
Though technically third-person, the series is essentially presented from Harry's viewpoint. So it can be argued that Harry describes the... positive physical attributes... of Cedric Diggory, Bill Weasley, Tom Riddle (whom the narrative calls "handsome" seven times), and teenage Sirius (in photo or memory form). seems to cause this. Both Ron and Seamus have referred to his "good looks" more than once. The narrative describes him as "handsome", and the narrative basically presents things from Harry's opinion.
Harry and Cedric's interactions in book four (mostly construed as them just being good sports, but people use it)
When Dudley says to Harry "Who's Cedric, your boyfriend?", Harry doesn't actually deny it... and Dudley only knows about Cedric because Harry was saying his name in his sleep (of course that could just be that on/off PTSD of his...).
It might also just be a teenage boy noting that other people are physically attractive. Female characters note that other female characters are attractive and don't get mistaken for gay.
When Krum first showed up at Hogwarts, Ron gets jealous that Malfoy gets to speak to him before Ron can. He even said he wanted Viktor to sleep in his room.
"We could offer him a space a space in our dormitory, Harry ... I wouldn't mind giving him my bed, I could kip on a camp-bed."
In the chapter The Unbreakable Vow in HBP, the Malay version states that Harry is surprised to hear Draco talking rudely to Professor Snape, who is usually 'dihormatinya malah disayangi', which literally translates to 'respected, even loved by him'.
Colin Creevey's fanboy crush on Harry.
Harry's massive boycrush on the titular Prince in HBP.
Hermione: For weeks you carry around this book - practically sleep with it.
Harry: I do not sleep with it!
Ron: Yeah you do. You read a chapter everyday before you go to bed - all you do is read that bloody book! *** That's not counting Ron sounding jealous
And the fact that Harry's boycrush is, by extention, on Snape, as he is the "Half-blood Prince".
Barty Crouch Jr. definitely seems to idolise Voldemort a bit too much. It's taken to the extreme in the film adaptation of Goblet of Fire when he actually wipes blood off Harry's arm saying that his blood now runs within the Dark Lord, before licking it off his finger.
Having been played by David Tennant, his performance in that scene is frequently described as 'eager,' to put it mildly.
Voldemort and Draco's bizare hug in The Deathly Hallows Part Two.
Snape's desire to look into Harry's eyes is suggestive, as this comic illustrates. Canonically, it's because Harry inherited those eyes from Lily, the only person Snape truly loved.
Lupin acts unfalteringly cheerful towards Snape no matter how negatively Snape responds to his presence in the Prisoner of Azkaban, it's clear he was trying to make amends for their school days but it is constant. On the other side Snape does kill a Death Eater who was aiming at Lupin.
Ginny Weasley is all but stated to have been Luna Lovegood's only friend at Hogwarts for years. And during the DA meeting in Deathly Hallows, the pair of them share the same armchair, Luna sitting on one of the armrests.