This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Garfield Specials
The sequence in the special Garfield's 9 Lives involving Diana's Piano. If the music doesn't get you, the ending will.
Sarah: That evening, I could tell Diana wasn't feeling well. So, I put Billy to bed early, and performed a whole concert, just for Diana. I'd never played better. When I finished, Diana didn't want to leave the piano. "Goodnight, Diana". Sometime, during the night, Diana managed to get down onto the keyboard. She laid down, put her face on her folded paws... and quietly passed away. It was Diana's testament to her love for my music.
From the same sequence, Sarah's final words spoken in the special, directed to the cat that's been sleeping on her lap as she told the story: "Would you like me to play something for you, Patches?...it's just as well..." She's clearly still mourning Diana, and all she represented to her.
There is a sequence in the television special Here Comes Garfield that qualifies as well. Before Odie is dragged away to certain death by the pound employees, Garfield lies next to him to comfort him. Also, Garfield's final lines before Odie is taken away really tug at the heartstrings. Then he cries silently.
Garfield: I'll see you, Odie. Sometime, somewhere... so long, old friend.
As Garfield says this, he hangs his head sadly. Odie then gives him one last lick, as if to cheer him up. Notice the little smile on Odie's face after he does that. It's as if he knows what's going on as well, and that he considers Garfield his friend too.
The song "So Long, Old Friend" is sad on its own, but it's also played over a sequence of Jon bringing Odie home as a puppy. Garfield, who's a kitten himself, meets and immediately starts playing with him. The happy scene of them having so much fun, coupled with the song, is heartbreaking.
The final scene of Garfield on the Town (based on the aforementioned storyline of the strip) in which Garfield awakes the next day afraid that his encounter with his mother the previous day could have been a dream, then we see she was watching him through the window of the house and quickly retires. Cue sad music, Garfield goes to the window to watch his mom leaving. Although it may have been the case of the Latin American dub because Garfield last words instead of "Thanks mom, for everything" were more along the lines of "Thank mom. Farewell."
In the Christmas special, Garfield - who we've always known as a selfish, greedy, gluttonous cat - gives Grandma Arbuckle a bundle of long-lost love letters from her late husband; she calls them "the nicest presents I could have received". And then Odie - who's always been taking the brunt of Garfield's abuse - give Garfield a thoughtful gift as well.
Grandma:[reading] "My darling; if the sea were of ink and the sky of parchment, I could not begin to write my love for you..."
Also from the Christmas special is a nighttime scene where the usual zany hijinks are dropped for a quietly poignant chat. Grandma reminisces about her deceased husband to Garfield, and confesses that Christmas was his favorite time of the year... it's also the time of year she misses him most. (Watch here)
Even more meaningful when you read about Jim Davis and learn that Garfield himself was based on Jim's grandfather.
The speech itself:
Grandpa was a proud man. A strong man. He was a good provider. We...never had much money, but there was always plenty of food on the table! And he always made something special for me and each of the children on Christmas. Men like him... they didn't feel that they could show much outward affection toward the children, but on Christmas, it was OK. I think...I think it was his favorite day of the year. (Her voice growing quieter) Sometimes I wake up in the night, and I can still feel his strong arms around me...this is the night I miss him the most.