Without a doubt, the Jim Henson Tribute, when Fozzy's reading the fan letter and says 'i'm sorry to hear your friend Jim Henson died'..gets me every time!!
As for in the movies, possibly Muppet Christmas carol, Kermit coming back from Tiny Tims grave, but the Muppets have a way of bringing out so many emotions, joy, laughter, and just like that..tears, and to be able to convey that emotion through puppetry..Wow..what an art!