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. However, Ed's relationship with Ling, and Mustang's rather heartfelt reaction to Hughes' death still add moderate Ho Yay fodder.
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 where it actually happens).
Ed and Ling do have a bit, especially in the scene where Ed carries Ling while they're in Gluttony's stomach.
Perhaps the most obvious example is Ed and Al. Besides their unconditional love, mutual dependence and sacrificing their lives for each other, there's Al's line (somewhat changed in the dub): "But there's one thing that I'm sure of. I want to touch you again, brother. Isn't it weird? We're this close, but the sensation of touching you, and the warmth of your body ... I can't remember them."
Episode 38 has them bickering like an old married couple and splitting up, only for Ed to start missing Al a moment later and going after him.
Even more obvious in the movie, with Edward calling in dreams both Winry AND Alphonse, and living with his real-world counterpart, while Al starts dressing as his older brother, dreams of being Heiderich and living with Ed, and finally leaves his whole world behind to be always with him.
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.
End of ep. 48 is also a bit shippy, though some are split on whether 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 it's telling that this moment comes at their last possible meeting, when they both know they might be going to their deaths.
Some of the official art is rather blatant as well:◊ ◊ ◊ ◊
Alfons Heiderich/Edward in the movie. Basically canon in the original script, where Ed was at the receiving end of both Noah's affection (more ambiguously) and Heiderich's. The booklet that comes with the special edition of the DVD even states that Alfons dies "with conflicted feelings towards Edward". There's also the implication that they were sharing the bedroom (which only has one bed), given that Heiderich's clothes are in Ed's room, in addition of this. Make of it what you want.
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.
Dante seems to be flirting with Rose in episode 49; calling Rose "exquisite" as she runs her fingers along Rose's neck. Of course, this is No Yay for a lot of viewers, given what Dante plans to do with her...
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. The arts and songs aren't canon, but are still pretty blatant shipper-bait from the anime team.