Hand Puppet

A puppet entirely operated by hand, usually with the puppeteer's hand inside. A common gag will involve the puppet acting implausibly independent of its puppeteer, often by being argumentative, abusive, etc. If it is independent, it's a Perverse Puppet or Demonic Dummy.

A prominent sub-type is the sock puppet, which is exactly what it sounds like: a Hand Puppet made out of a sock. Not to be confused with the Sock Puppet, which is an online identity that is fake like a sock puppet, not just a garden-variety poser.

Another sub-type, which is (somewhat disturbingly) common enough to qualify as its own trope, is the Dead Guy Puppet.

See also Muppets, which are generally more complex, involving both hands (at least -- some Muppets are operated by two people) for a more lifelike effect.

Anime and Manga

 * In Cromartie High School, Destrade High's Yamaguchi introduces a ventriloquist named Akira Nakao. He plans to have him as his right hand man, but quickly shifts the job over to Nakao's puppet, Mick.
 * Best Student Council: Pucchan & Lance
 * Midori Days had Takkizawa, a figurine fanatic, who, much to the protagonist's dismay, becomes fascinated with hand puppets.
 * Mubyou from Wagaya no Oinarisama always wears two hand puppets and sometimes uses them to talk to people...which doesn't change the fact that her punches can shatter concrete.
 * In Ouran High School Host Club, Nekozawa has a hand-puppet cat named Belzeneff.
 * Juri Kato of Digimon Tamers (pictured above) has a sock puppet that she often uses to express her opinions and feelings instead of stating them outright as if they were her own.
 * In Okusama wa Mahou Shoujo the female employee at Kashiwa Publishing uses one to speak with occasionally.
 * The main character in Maison Ikkoku at one point is recruited into a college club dedicated to putting on puppet plays.

Film

 * Mirror Mask starts with a pair of sock puppets arguing -- and for "sock puppets" read not only "made out of socks" but also "actually being worn on the puppeteer's feet". (Although actually actually, when the scene was filmed one of the puppets was worn on a hand as usual, to allow a greater range of facial expression.)
 * In The Hunchback of Notre Dame, Clopin has a small hand puppet of himself that acts fairly independently at times.
 * In Tom and Jerry The Movie, a child performer named Captain Kiddie has an extremely independent and sentient puppet.

Live Action TV

 * Sooty.
 * Several Doctor Who stories have used hand puppets to represent the alien monster of the week.
 * An alien ambassador in Timelash. (Astonishingly, it wasn't the most ludicrously cheap special effect in the story.)
 * The supposed Loch Ness monster in Terror of the Zygons.
 * 31 Minutos, a Chilean children's News Parody program, uses hand-puppets and sock-puppets prominently, and takes this trope to its logical extreme: using socks without even putting a minimal effort to convert them into sock puppets.
 * Not only socks, but also gloves got used as puppets at some point or another.
 * Jane's "truth snake" from Coupling is a hand puppet in the form of a pink snake that expresses her hidden negative thoughts when she's under the influence of mystery pills in one second season episode.
 * Good Eats, a cooking program starring eccentric chef Alton Brown, features quite a few puppets. The most prevalent would be those he uses for yeast, which are sock puppets (that burp).
 * Franklin, GOB's puppet from Arrested Development.
 * Gitmo on The Daily Show (a terrorist Expy of Elmo.)
 * Sifl and Olly.
 * Mr. Flibble in the Red Dwarf episode "Quarantine".
 * Craig Ferguson uses animal puppets on The Late Late Show. They most often appear in the show's Cold Open and are voiced and operated by Ferguson himself. Regulars include Wavey the Cajun-Scottish Crocodile, and Sid the Cussing Rabbit.
 * Kukla and Ollie on Kukla, Fran, and Ollie.
 * Many characters on Mister Rogers Neighborhood.
 * Many characters on Lamb Chop And Friends.
 * Several characters on Captain Kangaroo (classic versions).
 * The A-Team has an early episode where Murdock's latest tic is having a sock puppet named Sockey on one of his hands giving a running commentary to the team's latest job. BA gets so annoyed that he threatens both puppet and puppeteer to introduce them to his talking fist, Knockout.
 * The newscaster from Dinosaurs is actually named Howard Handupme.
 * Former CBBC mascots Gordon T. Gopher and Edd the Duck.

Professional Wrestling

 * In the World Wrestling Federation, Mick Foley once used a sock puppet named "Mr. Socko" to cheer up a hospitalized Vince McMahon in vain. The segment was a wild hit and Mick kept the sock around. Fortunately, his Finishing Move was placing a "nerve pinch" that put his hand into another wrestler's mouth so it fit perfectly that he'd stick the sock on his hand for the move and thus a cultural phenomenon was born.

Theatre

 * Punch and Judy
 * The Umbilical Brothers: ACTION FINGERS!

Video Games

 * This is an obtainable expression in Fable II .
 * Used for therapeutic interviews in Die Anstalt.

Web Comics

 * The main characters of the grim and strange Rocko & Socko sub-comic of The Parking Lot Is Full.
 * Elan from Order of the Stick has Banjo, God of Puppets.
 * God from Sinfest primarily expresses Himself with hand puppets.
 * El Goonish Shive once had a full-size filler comic with hand puppets dedicated to explaining a rewrite of the script that had resulted in a delay. There was also a Question and Answer strip that used them to answer a question about the dialogue between a couple of the characters during an off-panel moment.

Web Original

 * The entire cast of The Funday Pawpet Show
 * Most of the cast from Norman Tweeter Productions
 * Mike J, a contributor on That Guy With the Glasses, has the Super Pissed Video Entertainment Sock.
 * Zack from Echo Chamber opens Episode 1 with a...um...puppet? Sure, we can call it that. It ruins takes by cawwing loudly.

Western Animation

 * Mr. Garrison's puppet, Mr. Hat, from South Park. It's originally implied that Mr. Garrison is schizophrenic in some way, and uses Mr. Hat to act out his various repressed sides. The puppet is eventually phased out as Garrison becomes more disturbingly self-confident. It's kept somewhat ambiguous how sentient Mr. Hat actually is.
 * In The Adventures of Jimmy Neutron, Sheen ends up with his own public access show about hand-puppets.
 * In "Mother Nature" episode of Fairly Oddparents, Timmy's Mom became a weather woman and so Timmy's Dad decided to be both the mom and the dad by using a hand puppet that looks exactly like Timmy's Mom. Timmy's Dad can't get along with the puppet.
 * In the extended second season opening of Jimmy Two-Shoes, Heloise has one that looks like Jimmy, whom she has compliment on her ponytail.
 * In The Tick, The Human Ton has his good pal, the hand puppet Handy.
 * In the Droopy cartoon "The Three Little Pups", the wolf-as-dogcatcher uses a cat puppet to lure the pups out of their houses. The sight of a wind-up mouse causes the puppet to act like a real cat.