These two share a hug in season two, but it occurs after Reid has been held hostage, drugged, tortured, killed and brought back to life, and forced to dig his own grave by an UnSub with multiple personalities.
Hotchner and Reid stare at each other with strange frequency - and the boyband comment. It's probably because Reid's just so gosh darn shippable, but it's picked up a surprisingly vocal fanbase.
Morgan and Reid
Reid/Morgan was everywhere in season one, they were always together. In the first episode they're assigned to find the password for the UnSub's computer, they sit together in the UnSub's bedroom for a goodly amount of time.
In the third episode of the series, it's Reid's birthday, Morgan's all over him at the beginning. Plus, Reid is jumped by Morgan twice in season one alone.
There's also a ton of it in Season Four.
Morgan frequently calls Reid "pretty boy" and plays with his hair in one episode (It's early in 4x02 The Angel Maker.) Taking the Morgan/Garcia interactions into account can make it seem Ho Yay-ful. As the show goes on and as their relationship develops, they appear to share more with each other and have several moments that might indicate a romantic element, for example:
Morgan: (on the phone with Garcia) Hey, don't make me spank you!
Reid: Don't listen to him, Garcia, he's all talk!
Desiree Morgan: You're Doctor Reid, right?
Reid: (surprised) Yes?
Sarah Morgan: Derek talks about you a lot.
Reid: He does?
"Amplification", wherein Reid is infected with a deadly strain of Anthrax. To top off an episode already brimming with Reid/Morgan camaraderie, the writing team does the worst thing you can possibly do to induce massive amounts of Ho Yay: a montage of the team members reuniting with their closest loved ones after the outbreak, ending with Morgan waiting alone by Reid's hospital bed, waiting for him to wake up. 1, 2, 3, Awww...
Reid confides in Morgan alone about his nightmares, worries about his mental health and one of the cruelest things he was put through in school.
Speaking of nightmares, Reid wakes up from a particularly horrible one, screaming for Morgan during "The Instincts" Reid's nightmares.
In the season two episode "Revelations", after seeing a live video feed of Reid being tortured by Tobias Hankel, Morgan's first response is to punch a door and state, "I'm going to have someone's head on a pike for this." And aside from that, he spent most of the episode being uncharacteristically snippy with JJ, due to the fact that she was with Reid when he got kidnapped and wasn't able to stop the UnSub.
And calling back to "Revelations," in the season seven episode "Epilogue," the team discusses the killer's obsession with near-death experiences and Spencer mentions he had one when Tobias killed him. Derek is surprised, and perhaps put out: "You never told me that." I guess they share a lot. Privately. Offscreen.
It doesn't help that they are almost a textbook Uke and Seme respectively: the younger, prettier Reid and the tougher, macho Morgan.
Hotch and Rossi
Hotch and Rossi, so, so much. From their very first appearance, they put off a ton of Ho Yay vibes.
When Rossi returns to the BAU, Hotch greets him with a lengthy hug and a smile (from Hotch, Mister StoicBadass Team Leader). Hotch and Rossi are the only team members to regularly use each other's first names (Rossi is the only character besides Hotch's ex-wife and brother to call him "Aaron"), and while Rossi breaks the rules on inter-team profiling (he quickly figures out Hotch is separated from Haley) and generally acts like a kid unwilling to share, Hotch lets him off with a minor lecture instead of a smackdown.
In "Identity", they tag-team profile a homosexual dominant/submissive relationship while speaking in the first person, and they do it quickly and easily, finishing each other's sentences. If we take the conversation as reflective of the men, Hotch is dominant, Rossi is submissive.
Hotch telling Rossi he can't take Zoe's death personally in "Zoe's Reprise".
Rossi giving Hotch a much-needed (and overdramatic) verbal smackdown in "Omnivore":
Rossi: So you think this is your fault?
Hotch: (voice tight) It is.
Rossi: Well, here, use mine. (offers Hotch his gun) No, really, you've convinced me. You hung up on him, practically killed them yourself. Go on, get it over with. Don't worry about us, we'll get this guy without you.
Hotch: Dave, I had ten years to do something about this!
Rossi: Shaughnessy made the deal. The killing stopped, he closed the case and sent the BAU away. For ten years you worked on other cases, active cases-
Hotch: But I kept coming back to this profile.
Rossi: Hey, I was retired! Should I blame myself for every victim that got killed when I was on my book tour? Look, if you wanna end up like Shaughnessy, like Gideon, blaming yourself for everything, you go ahead. But that voice in your head? It's not your conscience, it's your ego. This isn't about us, Aaron, it's about the bad guys. That's why we profile them, it's their fault. We're just guys doing a job, and when we stop doing it, someone else will. Trust me, I know.
Hotch: (gesturing to the gun) You can put that away now.
The deleted scenes from "Omnivore" and "The Angel Maker" are so full of Hotch/Rossi Ho Yay. In the latter, Rossi checks to make sure that Hotch is all right upon returning to duty and after the season three finale, wherein he couldn't keep a lookalike for his recently divorced wife from dying; in the former, they share drinks after returning to Quantico from Boston and Rossi reinforces his previous smackdown.
Rossi at Hotch's bedside telling him they'll catch the Reaper in "Nameless, Faceless".
Their scene at Haley's grave in "Slave of Duty", where Rossi knows what Hotch has decided before he says anything.
And their banter from the end scene on the jet in "The Performer" is just beyond-adorable, mainly for Hotch out-Deadpan Snarking Rossi:
Rossi: I mean, I worshipped the Rat Pack, but I would never have killed for Frank or Dean.
Hotch: No, you just drank whiskey and smoked a lot of cigars.
Rossi: This from the guy whose favorite album is the Beatles' White Album?
Even the team kind of ships them. Morgan asks, in "The Crossing", "where are Mom and Dad?". JJ's response is "oh, Hotch and Rossi are still at the seminar in Boston". This is also the episode where Hotch, full of self-loathing after his divorce from Haley, decides that he and Dave are crap at being married and might as well be good at being divorced.
There's a scene in "Reckoner" at the end where Hotch and Rossi are on the plane and Rossi tells Hotch that he was lying about having slept with the UnSub's wife. It's supposed to be more of a moment for Rossi to tell Hotch not to make the same mistakes he did, but it comes off as sounding more like a reassurance that he didn't do something dishonorable that would affect how Hotch saw him.
The scene on the plane back from the case in "A Family Affair". And Jack at the finishing line calling Rossi "Uncle David".
The opening scene of "The Pact", where the team is badgering Rossi to use some of his vacation days, and he turns down all of their suggestions. Alex finally suggests he give them away, to which Rossi tells Garcia to check which Bureau members have military spouses and gift them the vacation days.
There is a moment that was very unintentional in the first season, but can sound a little strange (and hilarious). Morgan and Reid are having a sweet heart to heart about nightmares, and Morgan is sharing his. Reid asks, "What did you do to get over them?" Morgan's answer is "Gideon."
Emily, JJ, and Garcia have a fair amount of Les Yay. Garcia refers to both of them as beautiful and lovely, and Emily appears to reciprocate her flirting in the same casual way that Morgan does. Femmeslashers are also quick to note that JJ responds to Emily rather than Morgan after she's been cornered by and forced to shoot rabid dogs that, earlier in the episode, devoured another woman.
Also for Emily and JJ, it's Emily who comforts JJ after she kills Deputy Battle. Comes up again in "200". JJ hallucinates Emily coming to save her, and leaves a clue that only Emily would recognize.
And on a creepier note there's often Ho Yay between UnSubs working as a team and between UnSubs and victims.
Not to mention between UnSubs and the main cast, whenever one becomes exceptionally focused on the other. Tobias Hankle's interactions with Reid take the cake in this regard, especially when he keeps repeating "God gave you to me for a reason."