This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Muppets
"Pictures In My Head." Kermit's sense of nostalgia and loss is conveyed extremely well.
Kermit: I mean the only way we can raise that kind of money is to....... to put on a show. ...and I haven't seen the old gang... in a long, long time. ... I guess... the world sort of forgot about us."
It gets especially great when the portraits come to life and The Electric Mayhem starts playing. The lyrics so beautifully capture what was "lost" and how great those memories truly were... and how wonderful it would be to have them back.
Should we do it all again?
Make them laugh like we did then?
Back on stage where we belong
We could harmonize for one more song
It gets especially heartbreaking when Kermit gets a glimpse of Miss Piggy's portrait and sadly covers it again.
Rarely can the Muppets invoke such a strong sense of guilt as "Pictures In My Head", since in a meta sense, the audience is responsible for the Muppets losing popularity.
The moment when Walter, Gary, and Mary are trying to talk Kermit into doing the telethon. They each quote a line of the Muppet Show theme song . . . and then Kermit plays the final 7 notes very slowly and regretfully on the piano.
Kermit singing "The Rainbow Connection" and being joined by Piggy and then the rest of the cast. (And the in-movie audience. And probably more than a few of the real audience.)
When Animal starts drumming again, you will cry.
It's one behind-the-scenes as well: this was Steve Whitmire's first portrayal of the song, which was very strongly associated with Jim Henson.
The moment when the countdown is over... and the telethon is shown to have failed. Even though the ending quickly turns into a awesome and heartwarming moment, it really just hurts to see all of them go quiet, finding all their effort to have been seemingly for nothing.
Watching Tex Richman harassing the Muppets after the telethon failed. The way he gets in Kermit's face makes you want to punch the guy. The in-movie audience was appalled by his despicable behavior.
When Walter first enters Kermit's old office, he sees on one wall an assortment of photos of Kermit with old celebrities, the center of which is... Kermit with Jim Henson.
Just seeing what's happened to Fozzie without Kermit and the others is absolutely heartbreaking.
Hell, it describes anyone being made fun of for daring to like anything that's not brand new.
Real Life example: Jason Segel visibly tearing up when Bret McKenzie thanked Jim Henson after winning an Oscar for best original song.
Seeing the pictures of Jim Henson and knowing how much he'd love this movie, not to mention Kermit's "It doesn't matter if everyone loves us: we're a family" speech, if he were still alive.
The "Man or Muppet" number has a bittersweet ending in which Gary takes a bus all the way back to Mary's house and apologizes to her, then the two of them embrace.
For Mary's part, it's hard not to feel sorry for her. For all the support she provides when around with the Muppets, Gary being completely absent for the day that was supposed to be "theirs" (to say nothing of his forgetting their anniversary dinner) clearly makes her feel like a major third wheel. Even worse when you recall the entire reason for the whole trip in the first place was to celebrate her and Gary's anniversary, and visiting the Muppet Studios was more or less a glorified afterthought. Poor girl.
Jerry Nelson's very brief vocal appearance is a Tear Jerker in light of his August 2012 passing, since this was the final Muppet movie he lived to see and be involved in.
Hell, it was even this before he died. Just the fact that they got Jerry - who had mostly retired from puppetry at that point, and was suffering from respiratory complications which would claim his life not long after - to do this one brief vocal appearance just for the fandom to notice is Awesome, Heartwarming and a bonafide happy Tear Jerker all rolled into one.
In the first episode Piggy has an aversion to Elizabeth Banks appearing on her show. A flashback reveals just why: She publicly feuded with Kermit outside of a screening of Banks' film Pitch Perfect 2 that she was appearing at. It is all but outright said that this is the moment the two broke up a few months ago. Even better, we get to see both sides of their argument.
Bobo on his failure to sell cookies for his daughter: "At least it was a good learning experience for her. If you want something, don't count on Dad."
Kermit's speech about how Fozzie cheered him up when the former got passed over for a job he wanted so badly in episode 3 is a heartwarming tearjerker.
The hospital scene with Fozzie and Statler in "Pig Out". Especially when Statler says that Fozzie was the only one who came to visit - Waldorf couldn't come because he was scared of hospitals.
Earlier: "How do I handle hecklers? I'm a comedian. They're a part of the job. The part that keeps you from completely liking yourself."
Piggy's crying over her PR disaster with Reese Witherspoon in "Walk The Swine". It's one of the few times where her haughty shield is brought down.
Even if the fans didn't particularly like her, you have to feel a little bad for Denise in 'Swine Song'. She probably started the new year thinking that she and kermit were going to go farther and be better in their relationship, and over the course of 2 days, she gets blown off, finds him sleeping, and witnesses chemistry with her frog and his ex. You have to admit that any pig or person would feel betrayed seeing what's been happening.
In "Tail of Two Piggies", Gonzo mentions finding a box of Camilla's old things, which made him sad over their breakup again. She comes back to him at the end.
Kermit's trying to reconnect with Denise after them "taking a break" in Swine Song. You see snippets of him calling her, trying to get her to talk again. And then we see that she sent a box of "his stuff" back to his office. To anyone who's been through a breakup, you can tell Kermit and Denise are getting towards their last legs.