This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Muppet Movie
Gonzo's song "I'm Going to Go Back There Someday" in the desert.
Rachel Yamagata's version of the same, from 2011's The Green Album.
Kermit's epiphany immediately afterward: "Well then...I was lying when I said I never promised anybody anything. I promised me."
The final film appearance of Edgar Bergen (with Charlie McCarthy), who died shortly after filming, and to whom the film is dedicated. Bergen was a huge influence on Jim's early work.
Kermit literally put his life on the line to rescue Miss Piggy, and how does she repay him? By running off the instant her agent calls with a hot tip on a job. It's so depressing that the film itself falls apart as the only possible segue.
It's a little hard not to choke up watching Jim Henson's Kermit singing his iconic song at the beginning.
Kermit asks who Doc Hopper's friends are. Hopper says that he has plenty of friends, including Max. Max sadly shakes his head. The way Hopper says "Max...!?" in that disbelieving way really makes you feel for the guy. It's just a shame the moment of introspection doesn't lead to anything.