Btw, it's just been renamed The Paley Media Center.
I can come up with something of a list. In most cases, they only have some episodes of the shows, not all. Still it's a great collection!
Muppet Show
Muppet Babies
Fraggle Rock
Sesame Street
Tales From Muppetland
Several TV specials and appearances, including the 60 Minutes segment (A ton of stuff to mention here! And sometimes you have to go digging!)
Ghost of Faffner Hall
Puppetman pilot (very very difficult to find anywhere else)
Jim Henson Hour
Sex and Violence and The Valentine's Show
Tale of Tinkerdee (2 pilots)
Appearances Muppet performers made at The Museum (Q&A that sort of thing)
That's all I can recall at the moment. One thing they don't have yet is Little Muppet Monsters, now that would complete the collection!