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Zack and Maddie's slow dance in the episode A Prom Story, punctuated with background music by Kim Rhodes.
The song that plays while they're dancing also counts as not only heartwarming but also reflects on their relationship, particulary the lyric; I know I want what I can't have.
London's sentiment on a forbidden boyfriend; "I'd love him even if he were poor" in "Cookin' with Romeo and Juliet".
And then Moseby tells her that he approves of her forbidden romance, even if doing so costs him his job, because "if you really love someone, then you have to think of them before yourself". Whoever came up with the idea for this episode is a genius.
Then she goes on to repeat his advice in her I Want My Beloved to Be Happy moment - said moment being perhaps the most unselfish thing she has ever done. AAAAAAWWWWWWWWWWW...
Cody and Barbara Brownstein at the ending of "Orchestra".
In the episode "Books and Birdhouses," Cody is about to fail his woodshop final. Zack, who is for once top of the class, trades their projects while the teacher is out of the room because he fails all the time and getting an A means everything to Cody. In the end, Cody won't let him go through with it.
The Suite Life on Deck:
The episode when London visits her grandmother.
Mom and Dad on Deck has London giving her late birthday gifts to Mr. Moesby after spending the day following him around counts. They're exactly what he wanted, and it comes after Mr. Moesby's crappy birthday the day before. Also doubles as Narm Charm because of the jokes and sappiness throughtout.
From the same episode, there's Zack and Cody making up with their mom and dad for not being truthful with them, especially the part where the twins hug Carrie. Might double as Narm or Narm Charm too.
"So You Think You Can Date" has a nice ending full of Narm Charm. The entire episode was about Baily and Cody trying to make each other jealous with their new dates for an upcoming dance. In the end, both of their dates end up pairing up with each other, leaving both Cody and Baily alone on the dance floor. At this point, a Genre Savvy viewer would expect it to just end with Cody and Baily getting back together, and indeed they do start to dance with each other. But as Woody notes, it's very awkward, and it's obvious that they're not getting back together. Cut to a Ship Tease (no pun intended) with Moseby and Tutweiler, who throughout the episode have been trying to secretly recreate their broken high school years with this dance. They now both understand why this dance was so important to each other and, as they dance slowly together, see themselves as they were when they were teenagers.
"The Silent Treatment" has a sweet Zack and Cody moment. Cody has joined a monastery after breaking up with Bailey. Zack goes to get him and in the end gives him a surprisingly sweet speech to convince Cody to come back to the ship. Followed by a hug.
Zack: These aren't your brothers. I'm your brother. I care about you. I'm not leaving this island without you.
"Goin' Bananas" has the brothers admit to their insecurities caused by the other's acheivements. After admitting they didn't know the other felt that way, they hug. While Cody's wearing a banana costume.
"Snakes on a Boat" managed to get a LOT of crap past the radar but in the midst of all that, we also have Mr. Moseby saving Zack's life after he's bitten by a snake, in spite of all their differences. And considering what he had to do to save it, that's pretty impressive.