Pokebattles is a major affectional parody site. It parodies Pokémon, with a battle system identical to Pokémon Red. They always say "used" before attacks and multiple actions. They parody multiple other things including Star Wars; Luke is a character. Doompuff, the evil rabid Jigglypuff of doom, is The Juggernaut. A link to Red Version is here.
The LOLCat Bible Translation Project. It's exactly what it sounds like. Some parts are more affectionate than others, depending on the "translator", but it's generally good-spirited, often hilarious, and occasionally surprisingly well-thought-out (see the lolcat "A Mighty Fortress Is Our God").
The Election Night 2016 live show parodies Dr. Strangelove; Will plays himself as an analogue of title character, Felix plays General Ripper, and the hosts face the uncertain future with a sing-along of Vera Lynn's "We'll Meet Again" note The show was even supposed to end with Felix's character being Driven to Suicide upon Hillary Clinton's presumed win, but this had to be cut due to Donald Trump unexpectedly winning the election.
Episode 18 begins with Felix presenting his new radio play The Upset Governor, a parody of both Fawlty Towers and British radio plays as a whole.
Episode 52 begins with the show's producer Brendan James doing an impression of British documentarian Adam Curtis' narration style. (Curtis himself was later a guest on episode 65).
Some if these you actually have to be fairly familiar with the writings yourself to even get. For example, in the intro Isildur's death is blamed on the ring's treachery, which causes Mike to remark that being a bloodthirsty tyrant may have had something to do with it.
Kung Fury is a only a trailer as of January 2014, but is a Kickstarter project meant to turn it into a full film. It's a love note to '80s action films, but so much more! It has...well, just watch the trailer for yourself.
Parodies of music videos done by fans of the artist (and there are quite a lot), some examples being this and this. Although at first glance many of the Key of Awesome music videos seem to be making fun of the artists they parody, they have admitted they love most of the artists that they parody, and sometimes the artist loves them.
The sketch-comedy website LoadingReadyRun use this trope all the time. One of their better-known parodies is CSI:CSI - Internal Investigations. Replaced the discovery of a dead body with the stealing and eating of another person's sandwich.
Another skit along these lines was the Channel 101 skit "Cirque du Soleil — Sex Crimes Investigations", which spoofed both crime procedurals and Cirque in a goofy but fun manner.
Italian Spiderman is an affectionate parody of Italian B-Movies of the 1960s and 70s. The website is even complete with the fictional history of its production company, and details of how the movie was lost and recovered only in the early 2000s.
The Legend of Neil is a parody of The Legend of Zelda in specific, of video games in general and of the subgenre of animated series where someone from the "real world" gets trapped inside a video game.
The Jerry Seinfeld Program is a series of minute-long mock episodes of Seinfeld, using all the real credits and music and a greenscreen backdrop of Jerry's apartment, but exaggerating the characteristics of the show and characters to ridiculous degrees and applying the Seinfeldian Conversation style to inappropriate situations, like fundamentalist Christianity or agoraphobia.
Suparna Galaxy, Leigh Alexander's spoof of Mass Effect. On the one hand, it's a vicious condemnation of the game's reliance on turgid mathematical infodumping and thinly-veiled Dating Sim elements to look meaningful. On the other hand, only a slavish fan of Mass Effect could have written a word of it.
Retsupurae usually does this to their usual subjects (BillyMC, ElectricalBeast, Musclebomber2021, Cornshaq), usually portraying them as some sort of Memetic Badass. Their one-shot Let's Players, however, have usually been disliked in all seriousness.
Hilly and Hannah Hindi (of The Hillywood Show) are more or less devoted to musical parodies of Twilight (allfourofthe movies), Pirates of the Carribean, Harry Potter, and other broad targets. For their rap parody of Sherlock, they recreated the sets as accurately as possible, even filming at some actual locations from the series like the swimming pool seen in the final episode of season one. Hilly also does a scarily-accurate impression of Lady Gaga.
The Many Adventures Of Lividmanda is a parody of Survivor(in particular the Micronesia season) made by a poster on the snarky Reality TV message board Survivor Sucks. It was quite popular there, and the expression "I'm Livid!" was a minor meme among online fans of Survivor for about a year. Some of the jokes won't make sense if you're not familiar with past seasons of the show or if you're not familiar with Survivor Sucks, but the story can be enjoyed by pretty much anyone if you want a quick laugh.
This flash game is a parody of Little Red Riding Hood where instead of the big bad wolf going after the little girl to eat her, he gets bopped in the head by a piece of candy, sees a trail of candy, and decides to eat all the candy instead. The candy is dropped by a pair of children and the wolf, despite the fact that he could eat the children if he wanted to, hides from the kids when they look his way by pretending to be a bush. If you get caught, the ending (depending on how fat the wolf has gotten) will usually show the wolf meeting his end, such as being beat up by the children, having a bird poke a hole in his bloated belly so he flies around like a deflating balloon, or even being tossed into a pot to be cooked by a witch. Getting the wolf big as possible results in him falling on top of the kids and falling asleep from his candy binge.
While the Whateley Universe is generally parodying superhero comics (when not playing them straight), the story "Tales of the MCO" is a parody of the classic Quinn Martin productions, with a main character who is a parody of Jack Webb in Dragnet.
While it has more than enough angst on its own, his Grand Finale review of Scooby-Doo parodies how Atop the Fourth Wall has these world-endangering storylines but the comic (or movie in Critic's case) is always completed. Not to mention that the premise is suspiciously similar to "All Good Things", the final episode of Star Trek: TNG.
Two Power Rangers parodies, Mighty Weenie Pathetic Rangers and Post Psychedelic Power People made the rounds in the early 00's. They were close enough to the original scripts (and kept the most important parts as much the same as they could)) that fans could relive memories (this was before YouTube was an option) and diverted enough from the original that fans could have a laugh. The latter continued beyond spoofing Mighty Morphin' Power Rangers and even spoofed Zeo with Power People Zeeto, Turbo with Power People Turkey, In Space with Power People Lost In Space, and Lost Galaxy with Power People Lost Sanity. It's obvious that both creators were devoted fans of the show and based on conversations in newsgroups, admired each others' work. ArtistBros (the creator of the former) even said they were happy that they were the ones continuing beyond spoofing season 3.
Both even spoofed Fox advertisements for other shows with parodies of VR Troopers (VR Boopers), Sailor Moon (Sailor Goon and Sailor Spoon), and other shows that aired on Fox Kids. There were even early drafts for parody scripts.
Microwave Me started out as this, recreating his old experiments that he did from 1992 onward and adding new ones while giving references to Is It a Good Idea to Microwave This? and dOvetastic Microwave Theater, after about the fourth season, this was dropped because you're not really a parody anymore when you're microwaving things like CO2 cartridges and aerosol cans. Many one-time videos also create affectionate parodies of these shows, including a few even of Microwave Me.
The Happy Video Game Nerd: One towards The Angry Video Video Game Nerd and caustic critics, right down to the opening theme song of his earlier reviews and parodying a few of AVGN's reviews. Unlike AVGN and other critics, instead of bringing up awful video games that are best avoided, he talks about overlooked and under-rated video games not many played or heard of.
Limozeen, anyone? Their mixture of over-the-top Hair Metal Narm coupled with some solid Earworms could only be created by someone who has a legitimate appreciation for the genre.
The Peter Anspach Star Trek parodies each address how the crew of one of a major Trek show would go about the problem of changing a light bulb, in never-simple detail.
Echo Rose lovingly parodies YouTube vlogger culture, down to the low budget, stylistic editing, and the boisterous, talkative, young vlogging star... all while also telling the mystery of a small town.