Shows that include puppets from the 1980's include Great Space Coaster, Buster and Me, Today's Special, Eureka's Castle, Blizzard Island, Alf, ET, Gremlins Pee Wee's Play Houser and Return to Oz.
Sesame Street has been on from the 1970s on. "Captain Kangaroo" also had puppets in addition to the human Captain Kangaroo. Lamb Chop's Play-Along centered on the puppet "Lamp Chop". "Mr. Roger's Neighborhood" also had puppets.
The ones I remember from being a kid are:
- The Muppets (1976-1981)
- Fraggle Rock (1983-1987)
- Sesame Street (1969-present)
And some others I found from different places:
Roland Rat, 1983-1991 (England or Britain)
Terrahawks, 1983-1984 (England or Britain)
There's probably been a lot of others as well, but these are the ones I could remember and find.