The prom episode of Tiny Toon Adventures has several: the way Buster asks Babs to the prom and how incredibly happy it makes her, the two of them bringing Montana Max to the prom to cheer up Elmyra after he stood her up, Dizzy Devil's incredibly hot date Mitzi asserting she likes Dizzy because he's a "kind, sensitive, caring person," and Bugs saving his mentee Buster from being extremely embarrassed by his poor choice in dance moves.
Also Hamton's attempt to ask Fifi to the prom. He tries to break the ice by saying that some guys are shy asking out girls that they like. He then asks Fifi for input, only to scoff at how proms and dates are "sexist" and "outdated." Hamton says it's too bad she feels that way, because he was going to ask her to go with him. As he sadly walks away, Fifi (literally) lightning bolts toward Hamton, wraps her tail around him and kisses him, admitting to him that she thought no one would ask her.
"Thirteensomething" is probably the sweetest romantic episode for Buster and Babs:
Babs: I didn't think you missed me.
Buster: I did. I'm nothing without you. You're my better half.
Babs: Yeah, but my better half is nothing without your half.
Buster: Did you really mean all that stuff about your better half?
Babs: Lemme show ya. (cue makeout)
Also worth a mention is one episode where Babs goes to try her luck at an open mic night at the local comedy club. At the last minute, she finds out that she has to follow the performance of the in-universe version of Robin Williams. This makes her insanely nervous and when she does go onstage, she begins to bomb. Seeing this, the Williams Captain Ersatz comes back and helps her through her act, which gets tons of laughs. The episode ends with Babs giving him an enormous Glomp in thanks.
The ending of "Washingtoon", where the evil Moral Guardian is reunited with her "tooniness", who she hasn't seen in years. This gives her a sense of humor and she bounces off happily to Wackyland.
Just before Buster and Babs go to appeal before Congress, they stop in at the Lincoln Memorial. Babs reads off a quote from the Gettysburg Address, when Buster admits that it doesn't apply to toons and that they were a "lost cause." What follows can be considered the greatest motivational moment of Western Animation.
Abraham Lincoln: "Lost causes are the only causes worth fighting for... Stand tough in the face of adversity, let right be done, let truth be your guide, and most of all, never give up. Never EVER give up."
The Tiny Toons Christmas Special: Buster Bunny finds out that he really was important to the show, and he gets teleported back. After having this confirmed by Babs, he literally leaps off the film in joy, and gives Babs a super hug.
The endings to "Armoa Amore" and "Love Stinks" Even if Furball and Calamity couldn't stand being around Fifi thanks to her smell, it's sweet how they both made sure she'd have someone new to chase so she wouldn't be left heartbroken.
Who can forget "Fields of Honey"? Not only does Babs bring Honey's reputation back to life, but in doing so, Honey's youth is restored and she's reunited with Bosko after so many years. Considering the fate of the actual Bosko cartoon, it's Heartwarming In Hindsight.
Hamton cheering up a heartbroken Elmyra in Sepulveda Boulevard after Montana insulted her.
The ending to "Turtle Hurdle" where Tyrone Turtle, after escaping from Elmyra and spending much of the episode trying to cross a busy highway, finally gets to relax in a pond.
When Sneezer the mouse thinks Plucky, who is his hero on the school football team, is crushed to find out that Plucky is selling out his team to their rivals. Turns out it was an act and plucky was really helping buster with a plan to win the game. One of the most touching if often overlooked scenes in the show is when Sneezer talks to Plucky before he reveals he was a Reverse Mole:
Sneezer: "Say it ain't so Plucky. Say it ain't so."