Major-General Song

The Pirates of Penzance provides a lyric most redoubtable: The Major General's song therein is reckoned Stock Shout Out-able, And Mr. Gilbert's verses, as a vehicle for parody On many varied themes, are copied with particularity. To demonstrate the actor's elocution and acuity For rattling through fast-paced tongue twisters with full perspicuity, Sir Arthur's tune is catchy, too—though some can't name the latter's song, It's still become the model of the modern Filk or Patter Song.
 * It's still become, etc.

Because the tune in question is so very recognizable To make a Trope about it is a project not despisable-- And to be most laconic, any sort of TV Tropes Made of Win Archive-full song Is likely to be based upon the Modern Major Gen'ral Song.
 * And to be most laconic, etc.

Advertising

 * A Geico commercial has a guy singing the Major General Song, dressed in costume.

Audio Plays

 * In the Big Finish Doctor Who audio, "Doctor Who and the Pirates", the Sixth Doctor sings "I am the very model of a Gallifreyan buccaneer" (and other songs from Pirates, Pinafore, and Mikado are parodied).

Literature

 * TORN has one about Gandalf here.

Live-Action TV

 * One episode of Babylon 5 has Marcus and Franklin taking a long journey to Mars in the cargo hold of a freighter. After Franklin gets tired of playing Something That Begins With Boring (it doesn't take long), Marcus starts singing The Major General Song to pass the time.
 * At the end of the episode, he sings the entire song over the credits in place of the normal music. Near the end of the song, you can hear the crew trying to make him stop. No, not the freighter's crew, the production crew.
 * In the Studio 60 On the Sunset Strip episode "The Cold Open", the cast performs a sketch including a parody of the song: "We'll be the very model of a modern network TV show."
 * The Muppet Show staged a duet of the song with guest host and comedienne Gilda Radner and a seven-foot tall talking carrot. The scene bore an ironic resemblance to another scene in Pirates, as Radner had requested a six-foot tall talking parrot, but was misheard.
 * David Hyde Pierce's monologue, as host of Saturday Night Live, was a parody of the song.
 * In the Frasier episode "Fathers and Sons", Frasier, Niles and Leland Barton sing the first verse of the song. Martin tries to join in but confuses the lyrics, singing about a "scary hippopotamus" (instead of "the square of a hypotenuse").
 * In the Mad About You episode "Moody Blues," Paul directs a charity production of Penzance starring his father, Burt, as the Major-General. Parts of rehearsal and performance of the song are shown. When the lyrics slip Burt's mind, he improvises a few lines about his son. During The Tag, Paul and Jamie sing a verse about the show's credit roster ("Now the show is over and you can watch the credits roll").
 * Doctor Cox's "Rant Song" from the Scrubs musical episode was based on the Major General's Song according to the creators.
 * Used for Russian spies' elocution lessons in the Britcom Sleepers.
 * Geordi La Forge sings a few lines of it for Dr. Crusher when she's trying to persuade him to audition for her on-board production.
 * Spitting Image did a parody of it with Neil Kinnock, basically to mock the fact that he had a tendency to speak very fast (and whose opponents thought he was speaking a load of rubbish).
 * In a more memorable scene from Home Improvement, Al sings the first verse of it in what he thinks is a sound-proof booth. It isn't, and as a result, he recieves a round of a applause when he comes out.

Magazines

 * An old Mad Magazine featuring the Kennedy family in a musical had Dwight D. Eisenhower singing "I Am The Very Model Of A Modern Former President".

Video Games

 * In Mass Effect 2, Mordin is The Very Model of a Scientist Salarian.
 * Appears again in Mass Effect 3
 * Colonel Jade Curtiss in this Youtube video.

Web Original

 * Barack Obama is the very model of a modern U.S. President

Western Animation

 * In The Simpsons a sober Barney completes an obstacle course while singing this.
 * The Animaniacs has "I Am The Very Model of a Cartoon Individual".
 * Re Boot ended its third season with a recap of the entire season, set to the song's tune.
 * In an episode of Pinky and The Brain, Brain sings a typically megalomaniacal parody of the song.
 * In The Wild Thornberrys episode "Sir Nigel," Nigel Thornberry sings a pastiche of the song about his family.
 * In a Veggie Tales episode entitled "The Wonderful World of Auto-Tainment!", Archibald Asparagus sings the first two verses of this song when asked to sing about "Military Intelligence".
 * In Mickey, Donald, Goofy: The Three Musketeers, our heroes apparently crash a Penzance performance, as pigs sing some of the first lyrics.

Fanfic
"I am the very model of a monster-hunter general Whether threats are mundane or ethereal or temporal Thanks to the aid of my maid I have slayed them with a katana And made a vow until I have repaid the debt on my honour I'm happy in my scaly skin, and have a tongue that's prehensile Though my tastes in sex and sustenance are difficult to reconcile For my bedmate and my breakfast are both sentient mammalians (Incidentally, while I'm lizardlike, I'm technically not alien) I've been told that I should walk the boards and play a Shakespeare vill-i-an But Dickens' London is not ready for an actress so reptilian It's a shame because the name that I would gain would be the best I can Victorian, Silurian, lesbian, and thespian!"
 * A Fan-made Sorting Hat song lyrics.
 * "I am the Very Model of a disgruntled Harmonian".
 * A rant about the Doctor's policy regarding changing time.
 * With apologies to Neil Gaiman, a version for Vastra from Doctor Who:

Music

 * The Filk Song "I am the Very Model of a Heroine Barbarian", said to be "from Gilbert and Sullivan's little-known operetta, Xena; or, the Warrior Princess."
 * Tom Lehrer's "The Elements" is described by the author as "the names of the chemical elements set to a possibly recognizable tune."
 * Further parodied by the Amateur Transplants with "The Drugs Song"
 * "I Am the Very Model of a Usenet Personality".
 * "I Built a Better Model Than the One at Data General".
 * "I Am the Very Model of a Genius Computational".
 * "I am the Very Model of a Singularitarian"
 * "I Am the Very Model of the Modern Sadomasochist".
 * The Capitol Steps did a parody of this referring to US Attorney General Alberto Gonzalez, "I am the Very Model of a Mad Attorney General". Recently (in 2010), a slightly altered version of this made the rounds in Virginia referring to State Attorney General Ken Cucchinelli.
 * Earlier, they did one about George W. Bush ending with the line "I am the Very Model of a Modern Major Genital"

Theatre
""Hello, I come with letters from Her Majesty, Victoria," "Who, hearing that you're trading now, sang Hallelujah, Gloria," "And sent me to convey to you her positive euphoria" "As well as little gifts from Britain's various emporia.""
 * "Please Hello" from Pacific Overtures has the British Captain's part as a parody (all the captains sing in their national "hats").

Video Games

 * The plot of Iji summarised to the tune of the song: here.

Web Comics

 * Darths and Droids has a version here.
 * 21st Century Fox has this as part of a whole miniseries of Gilbert and Sullivan spoofs.
 * Xkcd gives us Every Major's Terrible, lampooning the stereotypes and downfalls of assorted academic fields. There are multiple renditions on YouTube by fans.

Web Original

 * Wikipedia, in a break with their usual sombreness, has two songs which use the tune (among many others).
 * Not one, but two Neopagan versions.
 * A "theater nerd" offers up A Very Model Halloween.
 * There's a Ben Drowned version here: Statue of the Elegy.
 * And, of course, TV Tropes has this very article.
 * There's a fan-made tribute to the eccentric Let's Player Raocow.
 * Modern Major Rarity.