Sometimes works pretend to be interactive when, by the definition of their medium, they aren't. You know what this means, right?
*Beat*note (Oh, right, wiki pages aren't interactive media; we have no idea what your mental response was going to be so we'll just have to pretend you said something relevant to the question.)
Anyway, this is common in children's programming (e.g. Edutainment) to encourage a form of Audience Participation. Sometimes, instead of a blank pause the work will have a chorus of voices chime in with the expected answer.
When this trope is used in a Show Within a Show, it could involve The Tape Knew You Would Say That.
Shows with Fake Interactivity have No Fourth Wall.
Compare But Thou Must, the videogame equivalent, where the interactivity allowed by the medium isn't utilised. Not to be confused with the audience shouting at Too Dumb to Live characters.
In the movie Thomas And The Magic Railroad, the audience is supposedly responsible for putting the cushion out to break the conductor's, played by Alec Baldwin, fall. This is averted in the actual series, however.
The TV show watched by Millie Fahrenheit 451 has the protagonist's wife Millie, who is utterly obsessed with her TV Room. Not a room containing a TV, mind you; a room where nearly all the walls are televisions. Her favorite show (and many others, no doubt) has the gimmick of mailing episode's script a few days ahead of time, letting viewers memorize their lines. During the show, a light in the corner of the screen indicates when the viewer is supposed to speak. All Millie thinks about are the characters of the show, and she even demands that her husband replace the final wall of the room with a fourth TV so she can feel more immersed. No Fourth Wall, indeed.
Mo Willems' "Pigeon" series of books, beginning with Don't Let the Pigeon Drive the Bus present this in literary format, encouraging the readers to shout out "No!" when the Pigeon begs to do something he's not allowed to do, like driving the bus. Some of these stories were later adapted for DVD by Scholastic and Weston Woods. There are other children's picture books that have adopted this format as well.
The Sci Fi Channel would run advertisements where they would ask the viewer to please place their hand up to the screen. There was then a sequence where a futuristic laser beam would "scan" an outline of a human hand. The voice would then say "You have been cleared. Thank you."
Parodied in Bloom County, as Opus learns English from the show. In the first of those strips, he responds to "Trumpet player" with "Terflump Gerflump"; in the second, he answers "Public servant" with "bozo". In both cases, Rogers just says "Good!"
In another strip, Oliver's Banana Jr. computer does the same thing, but responds to the TV by saying "Ted Koppel is a waffle". When Mr. Rogers says "Good!", the computer addresses the house: "MISTER ROGERS HAS GONE BANANAS!"
And aside from the occasional Fourth Wall break, Sesame Street avoided this as well for the most part. Then along came "Elmo's World".
There's also "Abby's Flying Fairy School", but the characters ask each other questions rather than the audience.
Drake & Josh both try to talk to the people watching the show. In a truly hilarious bit, Drake is warmly received by his audience and given a plate of cookies through the fourth wall, while Josh is both insulted and spit upon.
In another episode, Crazy Steve is watching Dora the Explorer, asking Dora why she would need to ask the audience something so simple when she could probably figure it out herself.
Subverted in Angel , which had a fairly dark take on this in the "Smile Time" episode. Puppet demons hosted their own show and used it to steal the souls of little kids. In The Teaser, a kid was watching the show and as the mom walked out of the room, the lead puppet watched her walk away and then talked straight to the kid. This looks like normal Fake Interactivity until that particular kid, and no one else so far, loses his soul.
Played with in Romper Room: The host could use the Magic Mirror to "see" who was watching, naming children who'd written to the show. Since this was a show franchise produced by local stations, it was likely that a given child watching might be called.
Pee-Wee's Playhouse, being a parody of the "kid's show" genre. As an interesting side-note, the plastic overlay from Winky Dink inspired Pee-Wee's "Magic Screen" segments.
Parodied in a Saturday Night Live spoof of Dora the Explorer called "Maraka", in which the title character asks about the meaning of life, the nature of free will, and the Robert Blake murder trial while acting as though the viewers are giving a specific answer. Maraka also becomes aggravated when the "audience" does not pretend to toboggan down a mountain.
In several of David Copperfield's TV specials, he would perform a magic trick with the viewers at home, largely involving a series of cards on the screen and asking the viewers at home to pick a card and then move around the cards until he figures out which card you are on. He isn't really interacting with the viewers at home, he's using instructions designed to herd the viewers to a specific card.
Sam on the 1986 VHS Rent-a-Friend would like to be your friend. 
An early (and iconic in Britain) example comes from Listen With Mother, The BBC's radio program for children in The Fifties: "Are you sitting comfortably?" (Pause) "Then I'll begin."
When the BBC moved to TV, it became Watch With Mother. Fifty-odd years later, the show inspired the villainous "Wire" in the Doctor Who episode "The Idiot's Lantern."
Tape: Ou est le plume de ma tante? [pause] Ou est le plume de ma tante? Student: La plume de ma tante est pres de la chaise de ma tante. As well you know. Tape: Oui, la plume de ma tante est pres de la chaise de ma tante. Student: How does this tape know what I'm talking about? Tape: Ou est la plume de mon oncle? Student: Le plume de mon oncle est bingy-bongy-boogy-bongy. Tape:[affronted] Non! Pas de tout! Je ne me connais pas "bingy-bongy-boogy-bongy." Qu'est-ce que vous dites?
Doctor Who Live: The Monsters Are Coming! used mostly live actors, but featured the Doctor in the form of pre-recorded footage of Matt Smith on a screen. Several times, the Doctor asks the audience to help him break the Miniscopes by chanting "Geronimo!" as loud as they can. Of course, the footage just continues regardless of what the audience is doing.
Sent up in Wonder Project J2. A selling point at the time was that Josette, the Robot Girl whom you have been tasked with raising, would respond in full voice to player input, which generally came in the form of simple "praise/scold" prompts. In one of them, if you praised her dancing ability, she would modestly deny her talent, insisting that since you'd taught her everything she knows, you must be a much better dancer, and asks for a demonstration. After staring out of the screen for a few seconds, she claps her hands and laughs happily, admitting that she can't actually see you, but she's certain you were fantastic!
Used somewhat bizarrely in Barney's Hide and Seek. If the player starts the game and then goes long enough without providing input, Barney will simply start walking toward the end of the level all by himself. He won't complete the actual objective of finding hidden kids or presents, but he will walk all the way from the beginning of the game to the end after only a single button press on the controller.
Steamshovel Harry. It purportedly is a game about jump physics where you have to save the earth from an asteroid that will strike in ten minutes. Unfortunately, the mandatory tutorial video takes ten minutes and you die immediately afterwards.
Hate Plus has a sequence where *Hyun-ae tells you to make a cake before you can progress. This is a real-world cake. The game suggests recipes for you and checks to see if the amount of time each recipe takes to complete has passed, but if you wait the correct time, *Hyun-ae has no way of knowing if you've actually made a cake or not (unless you tell her). There is an achievement for sending the developer a photo of you eating the cake with her, though.
Inverted in one Homestuckpanel. Homestuck actually is frequently interactive, with Flash animations and game segments, but once trolled the readers by displaying a loading screen, followed by: "You spend no less than 90 seconds staring at this fucking GIF image before you realize the actual Flash animation is on the next page."
Parodied in the Homestar Runner Strong Bad Email "for kids". Strong Bad demonstrates how bad of a kids' show host he would be with an Imagine Spot. He asks the kids to say "The Cheat", which they do (though one says "Christopher Columbus") and Strong Bad gives them an F Minus Minus regardless. Then when they fail to find The Cheat hiding behind a box (they say he is "right there" but do not specify), he flips out and threatens to kill them all.
Wiggum: "Well, yeah, sure, why not! I mean, it's my job, right? Ha-ha!"
This was connected to a contest the show was running in which viewers could figure out the assailant to win a prize.
Used in Stanley, mainly by the goldfish Dennis to quiz the viewers.
Similarly, the Fish character on the PBSKids series The Cat in the Hat Knows a Lot About That! does this in short segments called "Fish Facts." Played for humor, because the answer to the question is always demonstrated in the background by the actual animal while Fish is asking the question. "You're right! Next time, I'll stump you for sure." In the third season, however, the animals appear in bubbles surrounding the cat to try to make things a bit more challenging.
A mainstay of the recent Playhouse Disney programs My Friends Tigger & Pooh and Special Agent Oso
Parodied on one of the Show Within a Show programs that Meatwad watches on Aqua Teen Hunger Force. Puppets sing and flail about, occasionally directly addressing the in-universe audience in a demonic tone. None of the characters seem to notice this at all.
This is your left! Left! Left! This is your left! Left! Left! This is your left! Left! Left! This is your left! You're going to die!
The Disney Junior show Little Einsteins stars four child prodigies who, by the age of six, have mastered various musical instruments and forms of interpretive dance, but are still worse at problem-solving than your four-year-old is, and constantly needs their help. Er... sometimes, anyway. Can be Fridge Brilliance, since prodigies or not they're still just children.
Another Disney Junior show, Jake And The Neverland Pirates, is pretty much Dora with pirates and better animation. Features Peter Pan in the pilot and Captain Hook as a running villain.
Narrator: Ducky Momo needs to get to the other side of the Bumbleberry river. Can you help him find the bridge?
Kid 1: It's right there! Behind you!
Kid 2: To your left! Your other left.
Kid 3: No! No, not that way.... that's a candy wrapper.
Kid 1: Now where is he going?
Kid 3: How has he survived this long?
Played straight in Team Umizoomi. The team addresses the viewer as their "UmiFriend".
Super Why! has this, calling the viewer "Super You". With the Power to Help!
Another Playhouse Disney show, JoJo's Circus, had the main character and her "pet lion" Goliath, mainly to encourage exercise by asking the viewers to get up and exercise or dance with them.
Even in Handy Manny, ever since the start of season 3. They couldn't re-do the classic animation with the tools dancing on a stage. Instead they had a mash-up of different scenes from episodes with Kelly asking trivia questions to the viewers.
The animated series Wonkidoos uses this. Similar to Blue's Clues, childrens' voices are used to answer the question. Unlike most of these examples, they don't even give you time to answer the question yourself!
On Wallykazam!, Wally will quiz viewers on things such as what word starts with a particular sound.
Android phones often have a Google search widget that consists of a search bar. It looks like you can type into the search bar, but it will actually just open up the Google search app, and only from within can you actually enter input.
Although the "Google Now Launcher" subverts this primarily because it technically is part of the search app (the "Google Now" screen also shows up as a page within it)