I think his was the first celebrity I was aware of and thus the first celebrity death I was cognizant of despite being 5 years old. Many of the shows had little introductions by him, he was present on TV broadcasts of Muppet movies (which we had recorded on the VCR and watched too many times), and often the "making of" stuff for Sesame Street, Muppets, and related things were on TV. While I'm sure I didn't entirely grasp death at that age, I did understand that he was gone and not coming back, and there wouldn't be any more of those little specials where Jim Henson and a bunch of other puppeteers were being heckled by their own puppets they were holding up. I almost wonder if seeing all that garnered my appreciation more for the people behind the scenes than those on-screen or on-stage; I really didn't start learning actors' names until I was nearly in college, but I knew Jim Henson, Stan Winston, and Steven Spielberg when I was in 2nd grade.
The Muppet Movie is the best of the films in my opinion; it basically just takes road trip, throws in a dogging villain, and populates every corner with Muppets. The others tried to focus a little more on their plot stuff, which made them feel less focused when they did the Muppet chaos thing of ignoring the plot in favor of hijinks or songs. But the first three are all solid fun. Still haven't seen Muppet Christmas Carol. Muppets 3D at Disneyworld is a blast and I'm excited about the new movie.
Then there's the other stuff... so MUCH good stuff. The Dark Crystal is one of my favorite fantasy movies and captures the wildness I'd like to see more of in fantasy as opposed to LOTR rip-offs. Anyone who hasn't watched The Storyteller needs to see it on Netflix streaming before it vanishes; the Greek side made after Henson's death kind of sucks, but the older fairy tale bits hosted by John Hurt are each something special.
I'm also glad that Henson company is still doing good work today. Anyone who's seen The Hitchhiker's Guide to the Galaxy can appreciate the real animatronics used for the vogons, as opposed to CGI. I heard the actors certainly found it nice to have something in front of their faces to interact with. Where the Wild Things Are is probably divisive story-wise, but the special affects were brilliant. So like Nick said, there's a strong legacy, and I hope the new Muppets movie will end the whole "insert Muppets into existing story" trend they've had for a few movies, so we can get on with good stuff.
Cause I really fucking love the Muppets. I didn't get the show when I was young; it went over my head. I gotta watch the seasons at some point and laugh at what I was missing.