Pat Sajak (b. 1946) has been the host of Wheel of Fortune since December 28, 1981. He also briefly hosted The Pat Sajak Show, on which Jim Henson made an appearance.
Gonzo and Kermit appeared on Wheel of Fortune for a week in 1999 to promote Muppets from Space.
Pat Sajak appeared in Muppets Haunted Mansion as one of the singing busts.
Various spoof characters, including Pat Playjacks and Matt Playback, appeared on Sesame Street.