lonelygirl15 has had a number of these, from "Proving Science Wrong... with Lonelybeast and Danielgirl15", in which the two main characters acted the part of each other, to "Coming For You", a threatening video posted by a Shadow.
With The Angels provides two examples, "Sunshine Film Academy", presented in the style of a commercial, and "Lifetime Achievement Award", presented in the style of a music video.
And even then, the stories are all 'protagonist in a superhero setting' except for "Tales of the MCO' in which some of the main characters sit around and watch television. And heckle.
Part two of the Extra Credits video game addiction episode consists of, instead of their normal visual pun, fast paced, analytically style show, the writer for the show giving a monologue to the audience. This is because the issue hit a little too close to home for him to write, so he decided to tell his story instead.
Time Raider of Why My Little Pony Sucks usually did videos explaining why...well,you get it. However, the video about the Mare-Do-Well was not a review, but an analysis on why that particular episode was so hated.
His video of "Dragon Quest" counts, too. While he reviewed the episode, in the beginning and at the end he takes time to explain how this episode caused him to hate the cartoon and why it proved to him it had nothing to offer to people older than 8.
Welcome to Night Vale has a couple examples of this. The most obvious one is "A Story About You", in which the usual news style is discarded in favour of a second-person narration describing the day in the life of an 'ordinary' Night Vale citizen. "The Sandstorm, Part B", is also an example, as the majority of it is narrated by Kevin, Cecil's Desert Bluff's counterpart.
An even better example is "The September Monologues," which changes the entire episode formula. It begins differently, without the usual "Welcome to Night Vale" catchphrase, and ends without the usual "good night." The episode itself is a series of 3 monologues from various characters, each one with a brief introduction from Cecil. What is even more unusual is the lack of weather, (save 6 seconds of generic music that are immediately cut off.)
There's also The Weather, where the report stops and a song plays, typically around the climax of the episode.
Twitch Plays Pokémon Black 2 is the stream's first LP of a Pokemon ROM Hack to entirely replace a main series game, rather than being a randomized vanilla game.
"Until the Lion Learns to Speak" from Folding Ideas. Instead of analyzing stories and music, he decided to discuss Somalian culture because he's worried about Somalia's current struggles overshadowing their rich history. Especially since they were the first country and developed the first written language. At the end, he plays the Somalian song, that the title's named after, with his friend.
"Ski Patrol": A parody of an old instructional video, about ski safety.
"Dino-Sore Days": A parody of an early Disney short, starring Cro-Marmot.
"Ka-Pow!": A three-episode Spin-Off starring Flippy, Splendid, and Buddhist Monkey.
The HTF Breaks, a series of one-minute episodes.
Love Bites, a series of short Valentine's day skits.
Kringles: short Christmas episodes.
Smoochies: Animations with three options, all three of which result in the character dying.
The Annotated Series breaks up its main features (video game based movies or TV shows) with intermissions that are usually completely unrelated to the central videos but are of similarly poor quality. These are typically meant as Breather Episodes for the riffers (and by extension the audience) to use to warm up before the next feature, but sometimes the intermissions end up being so bad they usurp the main feature.
Kevin And Ursula Eat Cheap have the letters shows, often recorded in advance of con appearances as filler episodes, which generally do not include any food at all.