The original Fullmetal Alchemist manga (as well as its direct adaptation, Brotherhood) has surprisingly little (arguably no) Ho Yay for a shonen with a huge and mostly male cast. Perhaps it's precisely this absence of deliberatesubtext which has led the yaoi fangirls to see romantic overtones in Ed's relationship with Ling, and in Mustang's rather heartfelt reaction to Hughes' death.
On the subject of Mustang and Hughes: Academy friends, met up again in the Hell of Ishval, and Hughes signed on to 'support Roy from below.' Roy then went on a Roaring Rampage of Revenge against Envy after learning he was responsible for Hughes' death. He was distraught at Riza and Havoc possibly dying, but it's only with Hughes that he truly loses his cool (though this can be argued as being because Hughes is the only one who actually dies).
Though there's still those very rare moments that could be argued as being Ho Yay, such as this one. In all fairness the interactions between the Elrics are more "brotherly" in the manga though, not going to the full "Elricest aura" that the first anime had.
Or how Ed and Al are pretty much living emotional crutches to one another. Whenever the other is threatened or it looks like they're dead the other freaks out and does everything in his power to save/protect the other.
Ed and Ling do have a bit, especially in the scene where Ed carries Ling while they're in Gluttony's stomach.
Darius and Heinkel recieve a lot of this in fan works.
Greed and Ling have a lot of Ho Yay, too. In the Viz manga there is a line in which Greed says, "I'm glad I hooked up with you", and the whole "aibou" ("partners") thing...
Throughout the 2003 anime adaptation, Alphonse Elric and Scar share some moments that could be interpreted as Ho Yay, such as Alphonse asking Scar how he feels about him in episode 24 and Scar sacrificing his life to save Al in episode 42. And if that's not enough, the seiyuu are aware of it, too.
Not to mention Roy Mustang and Edward Elric in the movie. Mustang lives in almost total seclusion until Ed shows up again, then they both totally ignore Winry and Riza to see and fight alongside one another again.
Also in The Conqueror of Shamballa, there are the lines after Havoc and Breda leave Mustang's hut, and Havoc wonders if they should have brought Lt. Hawkeye with them. Breda responds saying that she wouldn't want to see him like this and "besides, it's not the Lieutenant the Colonel is waiting for." Word of God is that the script originally planned to explicitly say he was waiting for Ed, but thought it was better merely implied. But they would have made it explicit if there had been a novelization.
There's also the way Roy looks at Ed when he returns and Roy says "I always knew you were alive." It's suggested that he and Al were the only characters who didn't think Ed was dead; even Winry seemed to have given up hope.
Not just the movie: The only time Mustang blushes in the original series— that's right, Mustang blushes— was at the beginning of ep 44, after Ed and the newly-Philosopher Stone'd Al high-tail it out of Lior. Roy delivers a very... revealing line about his relationship to the Elrics, after which Ed gets a reaction shot where his eyes go wide and then he smirks slightly, and then Roy seems to realize what he just said.
End of ep. 48 is also a bit shippy, though frankly this trooper can't tell if it's promoting Roy/Ed, Roy/Maes, or Elricest. Roy and Ed talk about how they're sacrificing everything they've earned in the name of Hughes and Al (respectively), but there's an overwhelming sense of It Has Been an Honor and Roy finally seeing Ed as not a child whose innocence he wants to protect as much as possible, but as an equal. Likewise, Ed sees the Roy behind the "Bastard Colonel" facade. They both admit they're Not So Different, and this trooper does think it's telling that this moment comes at their last possible meeting, when they both know they might be going to their deaths.
Ed certainly spends a lot of time thinking about Roy's "cocky smile" and "witty remarks" in the anime. "I can just see his smug face now..." We know you can, dear.
Vic/Ed saying "Roy Mustang is dead sexy...in a miniskirt!"
Winry, Scheska. Good god, they wander the world together, have romantic strolls along riverbanks at sunset, and have the Tomboy and Girly Girl thing going on, and basically ignore what love interests they have to spend all their time together.
There's also a moment in "The Stray Dog" when they're charging past Mustang and co. on a motorcycle, driven by Winry, and Sciezka puts her arms around Winry with her hands in a very...revealing position.
Also, Winry and Paninya, in both the first anime and original manga/Brotherhood.
Don't forget the extent that Ed and Al go to protect and just stay with each other. Even ditching Winry in the movie.
In the anime Ed "has something he's been meaning to tell Al for a long time" but didn't because he was "afraid of how he would react". Love confession!
Dante seems to be flirting with Rose in episode 49; calling Rose "exquisite" as she runs her fingers along Rose's neck.
There's also a little bit of this between Ed and Alfons Heiderich, particularly in the moment before Ed returns to Amestris when Alfons takes his hand and makes him promise never to forget him. It's also implied earlier that they share a dresser and maybe even a room. It isn't much, but it's enough to make them one of the more popular slash ships among fans of the first anime.
Roy and Hughes have a decent amount. Their relationship gets a lot more focus here, including after Hughes's death, where it's made much clearer that Roy is losing sleep and weight from it, and is overall taking far less care of himself than usual. They also have some pretty shippy official art◊ and moments in the novels◊... and then there are their image songs, where they seem to more or less admit to having feelings for each other. They aren't canon, but are still pretty blatant shipper-bait from the anime team.