1. "Rainbow Connection" From 'The Muppet Movie'
There are a multitude of mind-blowing technical things going on the scene where we first meet the young Kermit the Frog, strumming his banjo and singing to the swamp. First of all, he's surrounded by water on all sides. Where the heck is the muppeteer? Not only that…how are they operating his hands as he plays a musical instrument? The quick answers are "underwater compartment for Jim Henson to sit in" and "radio controlled hands," but the most impressive thing about this scene is that those questions aren't the first things that arise in your mind.
Kermit himself feels so real, his physical performance is so subtle and his song is so hauntingly beautiful and human (especially coming from a frog) that we immediately stop asking questions and just accept what we're seeing. After this scene, we can't dismiss Kermit and the rest of the Muppets as felt puppets controlled by offscreen puppeteers. These are living, breathing characters, filled with soul, more layered and complex than most humans in movies. This is what makes the Muppets special.