The episode "Bad Wolf" does this by taking the Reality Show genre (and The Weakest Link) to its logical extreme. Ironically, many critics and fans assumed the point was to mock how terrible those shows were and not a tribute.
Likewise, the episode "The Unicorn and the Wasp" is an Affectionate Parody of murder mysteries, especially those written by Agatha Christie.
"Love & Monsters" straddles the line between this and Take That! of the show's own fan-base. It affectionately parodies the 'good' fans, showing them to be, if socially awkward and a bit geeky, ultimately decent, likeable people who come together and form connections with each other based on their shared affection and love for 'The Doctor' and what he represents. Furthermore, these connections allow them to express and develop their creativity and even fall in love with one another. The 'bad' type of fan, who treats fandom as it were some kind of joyless, ritualistic vocation, with themselves, naturally, the bullying egotists at the top of the hierarchy? Well, they're presented as a Doctor Whomonster. Read into that what you will.
Iris Wildthyme (a character in the spin-offs who may or may not be a Time Lady) has her own series of Big Finish audios; for one season, each audio parodied a different decade of Doctor Who (the 1990s one in particular is pure Eighth Doctor TV Movie).
The Carol Burnett Show did many parodies over the years that would qualify for the trope, but one of the most celebrated was the show's 1976 takeoff of Gone with the Wind, called "Went With the Wind" (with Burnett playing Starlett, who descends a long staircase wearing a green curtain with hanging rod), The costume was designed by Bob Mackie, and is now on display at the Smithsonian Institution.
Stargate SG-1 episodes "Wormhole X-Treme" and "200" are affectionate parodies of sci-fi tropes in general. For God's sake, they have Willie Garson playing an alien soldier! To be fair, he was a nebbishy television executive in these two episodes.
Somewhat of sci-fi tropes in general, but mostly of Stargate SG-1 itself in particular. The Show Within a Show was too much like the SGC itself to be regarded as a generic sci-fi show, and many of the jokes were at the expense of events in SG-1 itself that aren't all that common in the sci-fi genre.
Supernatural mocks the horror genre in "Hollywood Babylon", with some Lampshade Hanging thrown in. They also had "Ghostfacers", mocking Ghost Hunters, which was also A Day in the Limelight for two characters from a previous episode. Dean, at the end, admitted of the pilot for the show, "That was half-awesome."
"The Real Ghostbusters" was one big parody of the fanbase and its conventions (not to mention its obsessive insanity), though they had to make a bunch of the fictional fans male so as not to piss off the female fans too much.
Rome, Italian Style — Italian cinema, both neo-realist and whimsical, down to the dubbed dialogue the films were once saddled with in the U.S.
The flicks featured on Monster Chiller Horror Theatre. Once, Count Floyd realized during his show that Whispers of the Wolf was actually an Ingmar Bergman film, making for an entirely different stylistic parody within the skit (it's largely a spoof of Persona).
Neil Simon's Nutcracker Suite (his late 1970s output).
The extended Godfather parody.
CBC content was often spoofed, and was the basis for Bob & Doug McKenzie most famously.
Mel's Rock Pile (American Bandstand and the like).
Gangway for Miracles (The Miracle Worker).
Maudlin's Eleven (Ocean's Eleven).
I Was a Teenage Communist (1950s teen horror and the Red Scare).
The Merv Griffin Show - The Special Edition (the talk show cross-bred with the reedit of Close Encounters of the Third Kind).
Garth and Gord and Fiona and Alice (Goin' Down the Road).
Interestingly, Power Rangers RPM did much the same thing as Turbo and Ninja Storm and made it work pretty well, despite having the darkest subject matter since Time Force. One moment things will be dead serious, with particular emphasis on dead, and the next, you'll have characters asking questions like "why do our Zords have eyes?" and "Why do explosions appear every time we morph?" and of course "Is that really spandex?" (Answer: NO.)
Fred Armisen, who plays Prince in a recurring Saturday Night Live sketch, is a lifelong fan and did the sketch because he hoped it would lead to him meeting Prince.
Armisen seems to like getting in affectionate parodies of music - another sketch of his was about a father's Hardcore Punk band reuniting at his daughter's wedding, with hilarity and broken glass ensuing... Two thirds of the actors playing the band actually were in hardcore bands in the eighties (Armisen himself and Dave Grohl). While the characters never showed up again, Armisen apparently liked doing it enough that he also released the song performed in the skit as a 7'' single credited to the Fake Band.
The X-Files episode "Jose Chung's 'From Outer Space'" is an Affectionate Parody of the show and people who believe in aliens. Later Millennium would do the same with "Jose Chung's 'The Doomsday Defense'".
"Bad Blood" was also an affectionate parody of the show within the show itself, more specifically it focused on Mulder and Scully's dynamics and their investigating techniques, and it also parodied vampire myths and vampire tropes.
The Millennium episode "Somehow, Satan Got Behind Me" shows a censor going berserk on the set of a TV show obviously a parody of The X-Files.
JAG: Admiral Chegwidden, while on leave in "War Stories", gets persuaded by a Hollywood producer to act as technical advisor on the movie “Fields of Gold” which is a Navy-themed action adventure with a court martial. Chegwidden is a Fish out of Water as the real Navy differs quite a lot from the Reel Navy.
The Conditions of Great Detectives is an affectionate parody of most detective tropes and the genre as a whole. Note that the creator, Higashino Keigo, is a popular mystery and crime writer so ultimately he parodies himself at the same time.
Rutland Weekend Television had a few of these, such as The Old Gay Whistle Test ("Old Grey Whistle Test"), Rutland Five-O, and 24 Hours In Tunbridge Wells (one in a series of 'Classically bad American movies', including sailors singing and dancing).
One can't help but think that it was the exact building used in Scrubs.
The Buffy the Vampire Slayer episode "The Zeppo" is, like Enchanted, a parody of the show itself, using strictly Xander's point of view to show loads and loads of out-of-context In Medias Res snippets of Buffy cliches and tropes that any Buffy fan could tell would make sense in context if the full story was ever told, but come across as hilariously random, nonsensical, and melodramatic as shown.
The Charmed episode "Chick Flick" was an affectionate parody of slasher films, giving us Piper's immortal line "I'm being stalked by psycho killers and I hide in the shower?". "Charmed Noir" from the seventh season is the same for Noir Gangster films.
Dick & Dom in da Bungalow parodied lots of Game Shows for the finale at the end of each week's show, which would end with "creamy muck muck" [custard] being flung everywhere. They used current shows—Muck or No Muck, Who Wants to Be a Muckionaire?—and older ones, which the children competing had probably never seen, like Muckphrase (Catchphrase). They occasionaly parodied another genre, such as doing political talk show Question Muck (Question Time), the week after a politician had suggested that Da Bungalow was too lavatorial.
Batman: This article argues that the mere fact of playing a relatively ambitious live-action production of a Super Hero (viewed at the time as an inherently worthless material) had to be played as a superficial, deliberately light self-parody devised by mainstreamers who never even suspected that a rich timeless fantasy was lurking underneath.
Jimmy Fallon put a twist on jokes about American football player Tim Tebow with "Tebowie", who doubles as a loving spoof of Glam Rock-era David Bowie and sings Tebow-specific versions of "Space Oddity" and "Ziggy Stardust" that are funnier for deliberately patterning the lyrics after the structure of the original songs. (The former becomes a dialogue between Tebow and Jesus Christ rather than Ground Control and Major Tom, for instance.)
Modern Family's season 3 finale features a beautiful parody of telenovelas in general.
This was also done in Malcolm in the Middle when Francis (who was in Alaska by that time) got arrested and had to spend a couple nights in the local jail and finds out the sheriff, his wife and deputy have very convoluted storylines.
Japanese comedy show Akan Keisatsu (Featuring core Gaki no Tsukai ya Arahende cast members Hamada and Matsumoto of the comedy duo Down Town) features a section named "Tousou CHUU", parodying Run For Money Tousouchuu, a long-running game show also produced by Fuji Television. The hunters in game are replaced by a significantly larger amount of crossdressers (who are generally slower compared to the originals, though there're still one or two on par with them), all of which are led by KABA-chan. Losers (tagged by any one of them) not only get eliminated like in the original, but will be lipstick-kissed by them, with a photo sent to other participants. What makes it more terrible is that, up until recently, no player has won this game.
I Was A Sixth Grade Alien: The "Tarbox Moon Warriors" show is a goofy homage to Star Trek, but it's clear that despite sounding extremely silly and having laughably bad acting, writing and props, no actual hostility to Trek is intended, and Tim's love for the series is usually portrayed affectionately.