The way Layla earns her Enchantix. Valtor has blinded Layla, so Queen Ligea promises to heal Layla's eyesight with her scepter (after the Winx and her daughter rescue her). A little later on, Queen Ligea is gravely injured, but there's not enough sunlight for the scepter to heal both Layla's eyesight and the queen's health. Ligea's daughter tells Layla to use the scepter to heal her eyesight, as her mother promised her, but Layla instead chooses to heal the queen.
In Episode 25 of Season 4, when Morgana reveals that she is Roxy's mother. After Roxy releases her from the mirror, the two embrace each other.
Roxy: Mom, I thought you were—
Morgana: Shh. Don't say it.
At the end of Secret of the Lost Kingdom, when Bloom frees and finally reunites with her birth parents, Oritel and Miriam. She, her parents and Dafne/Daphne share a group hug.
One from Episode 3x12, where Flora earns her Enchantix. After she dives in after Rose/Miele, she sees Rose about to be entangled in some seaweed. Flora manages to catch her and places her in an air bubble to bring her back to the surface. Just before she places Miele in the bubble, she tells her, "I love you, my little blossom." The line implies that she knows she's about to die, but only very slightly (it could also be the river's poison in addition to the seaweed entangling her). Now, someone tell me: Why did 4kids change this line?!
In Episode 25 of Season 1. Flora is attempting again to change Mirta back into her human self. Musa and Stella are ready to give up, but Flora refuses and in one last attempt, she finally manages to change Mirta back! Just before Mirta changes back, she has a vision of her and Flora reaching out to each other and after she is back to her human self, she and Flora embrace each other.
The finale of Season 2. Bloom has been forced to turn evil by Darkar and the Winx and specialists have gone to rescue her. Near the end, just when Bloom is about to defeat them, Sky breaks the evil spell over Bloom by confessing his love for her.
The end of Episode 15 of Season 2. Musa performs a concert at Red Fountain, despite that her father had threatened to pull her out of Alfea if she does. The reason for this is Musa's mother died from illness when she was a child and the family couldn't afford medicine due to being poor musicians with music as their only source of income (he didn't want to see Musa in this position). At the end of the episode, Musa and her father make up about the argument they had earlier and a picture of Musa's mother appears above them.
The moments between the Winx and the Specialists in episode 2x25 just before the Winx go off to rescue Bloom. Especially the moment between Riven and Musa:
Musa: I guess you're above all that mushy stuff, right Riven? You don't need anybody? Yeah, so anyway... (Begins to walk away, only for Riven to suddenly grab her arm and hug her)
Riven: Do me a favour. I just wanna hear you say that you'll come back. That you'll come back, to me.
Thankfully, 4kids did not ruin that scene and it's just as heartwarming in their version.
Episode 2x23, when Flora finally confesses her love for Helia (with some help from Chatta).
When Tecna is finally found in the Omega dimension (Bloom is the one who finds her).
This moment◊ from one of the Winx in Concert videos. Basically, the video was about Layla and Nabu going against Icy and Valtor in an ice skating contest with L/N winning. And Layla, seeing how upset Icy is over losing, takes one of the flowers thrown at her and Nabu and offers it to Icy. Aww.
In hindsight, Stella is a big ball of heartwarming. She is very spoiled and vain and sometimes even mean. However, she clearly does not consider herself above commoners. By the second scene in the first episode, she wants Bloom to attend Alfea with her, she practically drags Bloom on a shopping spree in the third episode, she couldn't care less that the boy she loves is not royal and one scene in an episode of the season one finale implies that she's angrier at Sky for hurting Bloom. You don't expect that from a spoiled princess.
The Christmas episode, where Bloom's friends try to throw her a Christmas party to cheer her up since she's stuck at Alfea. Since Christmas is unheard of in their realm, they don't exactly get the traditions right, but they did try.
Riven, of all people, trying to comfort Timmy and the girls when they believe Tecna has died and trying to get Timmy (who believes she's simply trapped, not dead) to accept that she may be dead. Then, a few episodes later, the moment when Bloom finds Tecna and the two embrace each other. Finally, the slumber party at the end of the episode the girls throw to celebrate Tecna being back with them.
It's implied that Bloom and Stella have a slightly closer friendship with each other than the rest due to meeting first. The little moments that show this, like Stella going to Earth to retrieve Bloom when she leaves Alfea, are rather sweet.
"The Shark's Eye" has a lot of heartwarming in it. From Stella admitting her mistakes to Brandon and being apologetic, to her parents doing their best to be sensitive towards her feelings, to Riven singing a song to Musa (although she somehow joins him) and Musa realizing he wasn't cheating on her and being sorry she thought so.