You can't help but find yourself getting a little sentimental about Skipper being eaten by the Giant Snakehead in "Snakehead!". Of course, being a kid's show, it's obvious he wasn't gone, but still, if you look at the other penguins reactions, it's pretty hard to take.
There was also that part in the episode "Operation: Plush and Cover" where the chimpanzees, Marlene and Maurice are in the zoos souvenir and the chimps tell Marlene and Maurice that due to not hearing from Julien and penguins for quite some time on the mission to rescue, they'd have to assume the worst. Just the looks on Mason, Marlene and Maurice's faces is enough to make you choke up a little before the penguins, Julie and Mort bust out of the box that they were accidentally shipped to the zoo in.
The latter half of "Loath at First Sight" is heartbreaking for Kowalski. Everyone, absolutely everyone, even his closest friends, despises him to the core and his desperation almost hurts to watch. Gets doubly so if you've ever been bullied because that's exactly what it feels like if you're bullied: As if the entire world hates you for no reason.