The intro to the game is a Continuity Nod to that of the game before it, Phantom Hourglass. We start with a story being told through a slideshow, presented by Niko no less (and considering it's been over a hundred years since then, the guy REALLY hung in there). Link fell asleep through the story, which causes his master, Alfonzo, to wake him up by shaking him silly.
Chatting with some of the Phantoms in the Tower of Spirits can find some amusing results.
"YOU SEEM CUTER THAN USUAL. WHY."
"CAN'T YOU SEE I'M WORKING HERE."
"MY JOB IS TO SLOG THROUGH LAVA ALL DAY. BOO."
"MY TORCH IS THE LATEST IN TORCH TECHNOLOGY."
"THE PATH I'M WALKING HAS A SPECIAL MEANING."
"I WISH WE HAD A SPECIAL MOVE, TOO." "THE FOUR OF US SHOULD INVENT A SPECIAL MOVE."
It can be pretty funny watching the Wrecker Phantoms transform into the series' version of Morph Balls.
Transporting your first passenger, the bridge worker, results in unique dialogue if you mess up, contrasting from the others who use the same line if you do something wrong. Special mention goes to hitting the brakes too hard, bringing up the mental image of the bridge worker just being launched across the carriage:
Bridge worker:Oof! Go easy on the brakes, will ya?
After the Sand Temple, a cutscene ensues of Zelda and Link rushing towards Anjean excitedly, telling her what just happened. Zelda then asks how they find Malladus. A mere response of "I don't know" from Anjean causes Zelda to crash to the ground, which is pretty weird considering she's still a ghost a this point.
When we find out that the Demon King intends to possess Zelda's body, Zelda reacts with appropriate horror, and goes on a mini rant about how Link has to get her body back now, while she waits here for him to get the job done. Family tradition, after all. But what really sells it is her eyes, deadly serious as she floats closer and closer to Link, and you just know that she would be shaking him by the shoulders if she could. One of the only few times where you can see Zelda with such a face—she must really not want Malladus walking about in her body. Watch it here in all its glory.
Zelda: "Nooooooooooooo! The Demon King is going to run around in MY body? BLECH! That's too disgusting for words!"
The moment she and Link learn of her ability to possess Phantoms. Zelda manages to make the hulking suit of armor that was just this close to killing Link look both imposing and endearing. She ends the scene by declaring "We need to find my body—I mean, that rail map!"
Also, it's inherently funny, seeing a big, intimidating, walking suit of armor like a Phantom, doing girly gestures and the like.
There's a sidequest where a woman in Papuchia Village is looking for a husband, but she's rather picky and the only suitable candidate is the Chief of Whittleton. However, she's pleased with the choice and they become a couple. Later on in the game, you rescue a prisoner from Pirates' Hideout and he says that he cannot wait to meet his girlfriend who is waiting for him... back in Papuchia Village. Even Zelda points out how awkward the situation became.
Spirit Tracks has the perfect parody moment of your typical Shonen Anime: After Link and Zelda defeat Byrne/Staven, who then insists that This Cannot Be! since they're just human, Zelda proceeds to give him the stereotypical "With The Power of Friendship" speech, followed by Bishie Sparkle radiating from Link's smiling face. They proceed to giggle at each other, give each other High Five and everything seems lucky and merry and happy... until the music suddenly dies down as they turn and sees that Byrne, who's not quite finished off yet, has been ignoring them and took the exit in the back.
Made even better by the fact that during this scene Zelda is possessing the body of a phantom about 5 times the size of Link.
Link and (apparently) Zelda are both still having that happy expression. When they realize he left, Oh, Crap! takes over and they take off after him.
Zelda's boxing movements when saying that she wants to have words with Byrne after she gets her body back. Byrne's angry eye-open and glare off to the side only seal the moment.
The scene after Zelda regains her body mid-air and begins to fall. Byrne shouts "Go now! Right now!" and the heroic overworld music starts to play as Link runs forward to catch her...only to stop abruptly as Zelda just falls on top of him.
Going on a long quest to bring one of the Lokomos a massive, glittery vase... and then smashing it to pieces. His reaction is priceless, your reaction choices to his reaction are funny, and his reactions to both of those choices are downright hilarious.
Near the beginning of the game, after mopping the floor with Alfonzo, Byrne approaches Zelda in order to capture her. But wait! Link jumps in front of her to protect her from the evil man... only for Byrne to slap him several meters to the side, knocking him out instantly.
It's small, but during the confrontation between Byrne and Anjean, notice Link and Zelda's absolutely spooked faces when Byrne makes The Slow Walk right past them while ignoring the duo completely.
There's also their "wait, what?!" faces when Anjean casually reveals that Byrne was once her apprentice.
The Ocean Temple introduces us to a whip-wielding enemy called Snapper, who is dressed like a Dominatrix down to the kink mask and groaning in a very suggestive way when hit. For added fun, whip them endlessly.
When sneaking out of Hyrule Castle, Link has to distract some of the guards so Zelda can get past them. Since Link isn't much of a talker, he manages to distract the guards by staring at them.
In the final battle, Cole gloats and looks down at Link and Zelda as his theme music plays. Once he realizes that Malladus is going to take over his body, the music abruptly shuts off.
There is a young Goron who dreams about visiting Castle Town and meeting the princess. After you bring him to Castle Town, Zelda idly wonders if he'll ever get to meet the princess. Then she remembers that she is the princess.
.Zelda: "Nooooooooooooo! The Demon King is going to run around in MY body? BLECH! That's too disgusting for words!"