In the episode where Aquaman and Atom team-up, a white blood cell snuggles Aquaman, who pets him in return. However, Atom pointed out the cell is sensing him to see if he's a germ that needs to be destroyed.
Aquaman: Feels like a hug to me!
In "Invasion of the Secret Santas", Batman finds a present from Alfred, the nutcracker his parents gave to him years ago. Batman just smiles and thinks 'Merry Christmas' before heading off.
The Red Tornado finally feeling that Christmas spirit and becoming that much more human. Then he explodes. Don't worry, he gets better.
Also earlier in the episode, when Red Tornado tries his darndest to get that Christmas Spirit by setting up cheesy decorations and wearing an atrocious sweater, but especially when he gives Batman a mug that says "Worlds Greatest Detective" on it.
In "Hail the Tornado Tyrant", Red Tornado sheds a single tear at the loss of his son. It's made even more heartbreaking when he thinks that his tears are nothing but 'oily discharge'.
Earlier than that, Tornado Champion's emotional subroutine is activated, and his first words are "Father." He then proceeds to hug a startled Red Tornado (who hesitantly returns it), and the next few scenes show them bonding over helping others. AWWW...Pity Champion had to make a Face-Heel Turn.
Black Canary and Green Arrow's duet at the end of "Mayhem of the Music Meister!"
And that one moment earlier when Green Arrow was still in the Meister's thrall, he still couldn't bring himself to hurt Canary.
At the end of "Requiem for a Scarlet Speedster", Batman returns to Central City with Jay Garrick, Kid Flash and the previously-thought dead Flash, Barry Allen, just in time to spot Captain Cold, Heat Wave and Weather Wizard robbing a bank. The three are actually overjoyed, Weather Wizard even going "I promised myself I wouldn't cry". Seeing villains care so much about their main antagonist is surprisingly heartwarming.
In "Gorillas in our Midst", B'wana Beast was insecure about not being a good enough hero to be dating Vixen. When Vixen wanted to talk with him, he believed she wanted to break up with him. Afterwards, at the end of the episode, when Vixen wants to resume the talk, he spills all this out and tells her to get it over with. She asks him to marry her. Then in Siege of Starro part 2....
At the end of "The Power of Shazam!" when Batman does some investigating and finds Billy's long lost sister is very touching.
"Chill of the Night!" has to be the most intense episode of Batman: The Brave and the Boldto date, but it also has a great heartwarming moment — Batman is taken back into the past by The Phantom Stranger to a charity ball attended by his parents. He strikes up a quick friendship with his father, even helping him break up a robbery (which will lead to Thomas Wayne's death), but the real kicker is when he sees his mother, and all the tough, hard, no-time-for-emotions Dark Knight can do is hug her. Tightly.
In "Trials of the Demon", Batman, upon entering the past, meets Sherlock Holmes and has his identity perfectly discovered by a Sherlock Scan. Batman replies by jokingly identifying Sherlock based on his hat. At the end of the episode, Holmes asked Batman how he really knew who he was, to which Batman responded to his Real Life inspiration: "Everyone knows who you are. You're the world's greatest detective."
It's a given that "The Menace of the Madniks!" would have at least one when you see it's about Booster Gold traveling back in time to hang out with Ted Kord. Booster's reason for his initial trip back in time turns out to be helping Blue Beetle capture the Madniks, the ones he let get away, to give him some sort of closure before his death. And it's not just the pair of them, as by the end of the episode they and Batman have unexpectedly grown much closer together, which makes the ending when they leave all the more bittersweet. Finally there's Booster's farewell, in which he grips Ted tightly in a hug and says "Goodbye, old friend", as well as Batman and Booster Gold being shown as better friends after returning to the present.
In "Mitefall!", the conversation between Ambush Bug and Batman. Borders on Tear Jerker.
Batman: So, this really is the end?
Ambush Bug:'Fraid so. At least you can say you had a good run.
Batman:A great run.
"Goodnight", in which we see almost every character, good and bad, have a little goodbye party, before the show is canceled. All topped with Batman telling that, so long as evil exists, he'll be there to stop it even in the next show.
Also, you can see B'wana Beast reunite with Vixen.
Thanks to Batmite's Reality Warper interference, we get to see Batman with a wife and daughter for a brief moment.
"Joker: The Vile and the Villainous!" gives, surprisingly enough, one to the Clown Prince of Crime. It's oddly adorable seeing that even Joker has his heroes and and that he genuinely respects and CARES about the Weeper.
And it's much nicer than the comic it's based on (Joker #2 from the Silver Age) where the Joker just wants the Weeper to succeed so he can reap the spoils of the plan and drives the Weeper Laughing Mad. Here the Joker actually—in his own way—cares about the guy.
The relationship between Batman and Superman in "Battle of the Super Heroes." It harkens back to the Silver Age when the two were the best of friends and it shows: although Superman spends most of the most of the episode brainwashed into being first a jerk and then becomes outright evil, Batman is one of the few to still stick up for the guy even after members of Supes' own supporting cast like Lois Lane and Jimmy Olsen lose faith in him; reasoning that he can't be doing this of his own volition. When Batman does eventually confront Superman, there's no ill will or malice in him. Everything he's doing is to save his friend (and for that matter, his reputation).
Batman is also able to get Superman to hesitate for a moment asking him what Ma Kent would think of his actions. Jerkass or not, Superman loves his ma.