In the November 22, 1975 episode, Scred starts flirting with guest star Lily Tomlin. Tomlin finds it difficult to have her name linked romantically with a puppet. Scred gives the audience a rather confused look, but tells Tomlin that it's no problem.
When Raquel Welch hosted the April 24, 1976 episode, she pointed out that, as puppets, the Gorch characters did not exist below the waist.
Episode 101: Kermit is drinking milk through a straw. He looks at the camera and says, "Think about this, friends," referring to the fact that he is a puppet and can't really be doing what he appears to be doing.
Episode 307: When a bewitched candle was creeping across Kermit's desk, Kermit blows out the flame on the candle for it to stop moving. He laughs as he looks at the camera and says, "Think about it, folks," referring again to the fact that he is a puppet and can't really be doing what he appears to be doing.
Episode 508: This episode features several references and inside jokes about the Muppets being puppets, including:
Kermit telling the audience that the show will have a change of pace and be a puppet show.
Gonzo asking Kermit and Fozzie Bear what a puppet is, and after Kermit and Fozzie have difficulty explaining to Gonzo what puppets are, Gonzo remarks that it's such a stupid idea that he wouldn't even do such an act. After he leaves, Kermit says, "I didn't have the heart to tell him."
"Secrets of the Muppets": This entire episode is filled with explanations about how puppets work and jokes about the Muppets being uncomfortable with their identity as puppets. Whenever someone mentions the word "puppet," the characters gasp in horror; Bean even screams, "He said the 'P' word!" When Gonzo hears Jim Henson explaining how Gonzo works, Gonzo denies it, telling the audience, "This man is deranged!" When the camera pans out, revealing the Muppet performers under the Muppets, they freak out all the more. However, at the end of the show, the camera pulls back in to again hide the performers, and to the Muppets' relief, when they look down, they can't see their performers anymore. Jim explains that with the Muppets, "the fantasy always wins."
In a 1988 episode where Telly receives a visit from his Fairy Godmonster (Andrea Martin), Telly, misunderstanding her intentions, says, "And you're going to turn me from a puppet into a real live boy!" (YouTube)
In a behind-the-scenes feature for the DVD release of CinderElmo, Ernie and Baby Bear point out that unlike their fellow actors, they never blink (claiming it's an "acting skill").
In a Global Grover sketch, Grover plays with a marionette, remarking that it must be great to be a puppet.
In a Smart Cookies episode, "Making Whoopie in the Library," Cookie Monster, looking for something with strings to catch The Crumb's flying whoopie pie, gets a toy gorilla marionette. Chipowski says, rather unplussed, "A puppet?" After the inevitable failed attempt, he says, "Of course it didn't work. How can a puppet catch anything? It's just a puppet!" Cookie Monster scratches his head.
"How to Pick Up Girls": Earl and the Baby enjoy a puppet show, while Fran insists to Earl that puppets are just for kids, prompting Earl to (unsuccessfully) try to convince Fran that adults can enjoy puppets as well.
"We Are Not Alone": After Fran finds out that Robbie had tricked Earl into recycling and spreading enviromental messages on television, Fran tells Robbie that he can't just manipulate Earl like some puppet on national television.
The Muppets on Puppets: When Jim Henson mentions that Rowlf is a puppet, Rowlf tries to convince Jim that he's a real dog. Rowlf is practically traumatized when he looks down and sees a person operating him.
The Muppets Celebrate Jim Henson: At one point, the Muppets notice that there are "guys" underneath them, following them around -- and when the Muppets move, so do the guys. After a few seconds of this, Fozzie says, "Stop looking at them, even -- it's too weird." The Muppets then ignore their puppeteers for the rest of the show, just as they always have.
In Tales of a Sixth-Grade Muppet, Danvers' dad says that he's tired of working for his boss "like some kind of puppet" at the breakfast table the morning Danvers finds himself a Muppet. Danvers snaps, "I heard that!" Throughout the series, characters also notice Danvers' flip-top mouth, foam skin, and flaily arms.
The Tonight Show: Dr. Teeth informs Johnny Carson that as a musician, he doesn't get many girls because he's a puppet. He also notes he doesn't smoke, since he doesn't have any functional body part to smoke with.
The Vent Event: Fozzie and Kermit provide commentary for "Dr." Jerry Nelson's description of how the Muppets work. Nelson goes on at length until they can't take it anymore, and Sweetums whisks him away.
Reading Rainbow: Kermit appeared on July 8, 1985 looking for pig books in a library to find out how to handle a certain pig he knows. He uses pig books to convince LeVar Burton that he's there for pig classics. One of these books is "Pigochio, which is about a puppet who wants to be a real pig. "It's a pretty silly idea."
Presenting the award for Best Animated Short Film at the 1985 Academy Awards, Kermit and Scooter have trouble opening the envelope. Although they don't directly reference the problem, they heavily play up the fact that "characters like us" can't get the job done.
The Arsenio Hall Show: Rowlf appeared on May 22, 1989 wearing a sling because he had no one to perform his right hand, as he explained to Arsenio. On May 4, 1990, Kermit complained that he hadn't met Connie Chung backstage because "They keep me in a bag."
Jimmy Kimmel Live: Fozzie guest starred on the May 13, 2005 episode. Ozzy Osbourne was sitting next to Fozzie, and complained "What am I doing, talking to a fucking glove puppet for?" Fozzie appeared quite insulted.
Today: In an April 2, 2009 appearance, Elmo says that he doesn't know anything about puppets.
The Bonnie Hunt Show: In an April 7, 2009 appearance, Elmo and Abby help build paperbag puppets - the two are intrigued by the concept of puppets.
Five Minutes with: In outtakes shown for the segment, Matthew Stadlen asks if it's okay to see the black arm rods on camera. Grover whispers to him, "I am a puppet."
Good Morning America: When Roscoe Orman comments that he originally thought Sesame Street would be a fun, short job where an actor can "play with puppets," Abby Cadabby laughs, then says "What?" Following that comment, a heated dispute erupts between Zoe, Grover, and Abby about how they have never seen puppets on Sesame Street before.
Suffolk University: At Suffolk University as part of promotions for The Muppets, Kermit, David Hoberman and Steve Whitmire appeared in a lecture, along with showing a few clips from the film. When asked what it was like being immortal, Kermit replied, "It's an odd place to be...It's one of those things that I rarely deal with in our work because it gets too strange. But, you know, what are we all but inanimate objects in the end? There's something inside of us that gives us a spark, and at the end of the day we get put in a box and shoved in a closet."
Puppeteers of America's 75th Annual National Puppetry Festival: During their guest appearance at the festival, Steve Whitmire addressed to Kermit as a puppet, to which Kermit replied with his trademark chagrined expression. He then introduced Whitmire as his puppet.
When the Muppets appeared on Saturday Night Live, Kermit guest starred on the Weekend Update segment "Really??!!?? with Seth." When Seth Myers apologized for saying the word "puppet," Kermit explained that he was a Muppet, and that puppets are things controlled by a human, while he is actually a real live talking frog.
When Miss Piggy, Kermit and James Bobin were interviewed at a press conference after the London premiere of The Muppets in 2012, Kermit said at one point, looking down below him, "You wouldn't believe what goes on under here." Miss Piggy looked below her as well and shuddered.
At TED2012 on February 29, 2012, Scooter delivered an entire speech about puppets vs. computer generated characters. Throughout the talk, he referred to the Muppets as being puppets, even going into detail about the materials they're made of.
When GermanSesamstrasse characters Pferd and Wolle appeared on the show DAS! in 2012, with their performers about to be interviewed as well, the two characters confirmed that "there are puppeteers hanging out of us!"
When the Sesame Street characters appear in JD's fantasies in theScrubs episode "My ABCs", JD's diagnosis after consulting Ex Ray's x-ray is "You have a hand inside you." Ray concludes that this explains many things. In the same episode, Oscar the Grouch, as the new Chief of Medicine, warns JD "I'll be watching you, John Dorian! My eyes never close!"
During Kermit's speech at TEDxJackson, he noted that it took a lot of people to bring his speech to the conference. "Why at this very moment, as I speak, someone has a hand in everything I'm doing up here." While giving the audience a moment to laugh, he gave himself a lookover and noted, "And I'll be the first to admit it moves me."
The Muppets' appearance at San Diego Comic-Con to promote their new show saw them on a panel alongside their puppeteers. This resulted in several jokes made in reference to their puppet status.
At one point, Fozzie is encouraged to tell a joke for the audience. As Fozzie thinks for a moment, Rizzo shouts out, "Come on, Eric!" Fozzie (and Eric Jacobson) glare at Rizzo before refusing to tell a joke.
When a question is asked about Kermit, Rizzo looks down below his performer Steve Whitmire's chair and comments, "He's in a box!" Gonzo adds, "I probably shouldn't say this, but Kermit is half in the bag right now."
After Steve tells an anecdote about performing Kermit for several hours at the Rose Bowl parade, he comments that it is a rough job. Gonzo agrees, saying it is very uncomfortable, prompting laughter from the audience and Muppeteers upon realizing the implication of the statement.
On a February 1, 2016 appearances on The Late Show with Stephen Colbert, Kermit and Stephen Colbert ponder life's biggest questions. Colbert wonders if we all have free will or if someone's controlling us. Kermit gives himself a look over and replies, "I guess I never thought about it."