Okay, I know that EVERYONE mentions the "Saying Goodbye" sequence from MTM, and I am going to as well. However, it is a specific moment in that song that touches me--At the end of the song when Fozzie sings his verse "...You're in my heart, so until then...wanna smile, wanna cry...saying goodbye..." Do you hear the little choke in his voice during that? ALSO NOTICE, and maybe it is just me over-analyising, that Fozzie is the only one in that song who is all by himself--alone--while he sings. Sitting in the dark little train car clutching his teddy bear. Maybe he was singing to teddy.
More favorites:
--Follow That Bird--
The scene where he says goodbye to his friends on Sesame Street. That whole scene, ESPECIALLY the dialogue between Bird and Oscar:
Big Bird: "Well, goodbye, Oscar."
Oscar: "Why, why that's the nicest thing you've ever said to me." (brushes his hand across his brow)
Also the dialogue between Big Bird and Snuffy when they say goodbye; "One Little Star" with Big Bird, Snuffy and Olivia; and the scene after "I'm a Bluebird" when the kids sneak backstage to see Bird in the cage and the close up of the tear rolling down his beak (that gives me GOOSEBUMPS everytime!); also, the bit at the end when everyone is back together and then we see Bruno walking Oscar down the street and Oscar says "Once more around the block, Bruno. Yeah, I gotta walk off some of this happy stuff." The Bruno stops and looks up the street at the neighborhood playing and stuff, to which Oscar looks Bruno straight in the eye and says "Brunooo, come ooon." It was just kinda sweet on Bruno's part.
--The Muppet Movie--
Kermit's famous monologue at the ghost ranch; Gonzo's "I'm Going to Go Back There Someday" and the whole desert scene, especially Kermit's conversation with his conscience; "The Rainbow Connection"
--A Muppet Family Christmas--
The scene when Doc talks to a sad Kermit and offers to go looking for Piggy; When Robin gives Grover the Fraggle pebble; and one of my ALL TIME FAVORITE tear jerking moments........... at the very end of the special when the camera cuts to Jim Henson and Sprocket watching the Muppets from the kitchen and says, "It sure looks like they're having a good time out there, Sprocket. I like it when they have a good time." PROBABLY ONE OF THE GREATEST MUPPET LINES EVER!!!