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The opposite of this, where a character makes an equal (or, at least, necessary) contribution, but remains obscure or overlooked, is Stuck In Their Shadow.

Compare and contrast with Face of the Band and I Am the Band and My Friends... and Zoidberg. Also contrast The Pete Best.

It must be noted that in terms of musicians, particularly Rock bands, that the rhythm section (i.e. bass, drums, sometimes rhythm guitar) is the foundation upon which everything is built, so while many drummers or bassists may not be prolific songwriters or singers, many singer and guitarists acknowledge that the sound would be nothing without them.

Compare to Breakup Breakout.

In-Universe examples only, please. It is almost always controversial to list any real-life musician here.

Examples

Anime and Manga

Tenchi of Tenchi Muyo! gets a bit of this. He's the title character, but the show is really all about the girls; Tenchi himself is primarily relevant as a MacGuffin for them to fight over. Of course, one translation of the title is "No Need For Tenchi". How much of this he has depends on the series, and how far through the series one progresses. In the main OAV series, for example, he ends up being revealed as the reason all known universes were created, not to mention more powerful than the beings responsible for their creation.
Despite being Second in command of the SOS-Dan, Itsuki Koizumi is the least developed, least recognized and least liked of the five. It really doesn't help that all the merchandise is for the girls. So it ends up being "God, God's boyfriend and narrator, the Emotionless Girl, the one with the rack, and... that other guy."
- As far as purpose goes, Yuki usually gives out most of the 'facts', explaining what's going on, whereas Itsuki usually mused on ideas and philosophy. As the story went on, Itsuki had said about all of value he could say, so only Yuki was left to offer any real exposition. As far as what they bring to individual adventures, Yuki is the most useful as a Reality Warper, Mikuru herself is almost completely useless, but her adult self is the driving force of several plots (almost always those involving time travel), and Itsuki... uh... knows rich people.
One of the main criticisms of Sakura Haruno from Naruto is that she suffers this in relation to Naruto and Sasuke. She was introduced as the third member of the Power Trio, but as the series went on, her relevance to the central plot reduced.

Comic Books

There were issues of Cable & Deadpool in which Cable's entire role was basically to appear at the beginning and give Deadpool a mission. And a stretch of issues about Deadpool trying to find Cable in different dimensions. Eventually they literally crossed Cable's name off the cover◊ and replaced it with the name of a random guest star. Some of it was merely due to editorial mandate that allowed Cable to be busy, missing, or even killed off in the X-Men titles, leaving the writers of the book he was nominally headlining little recourse but to work around him, but even when Cable was available it often seemed like they were more interested in writing a Deadpool book that Cable was shoehorned into by, you guessed it, editorial mandate.
Similarly, in most Blake and Mortimer stories, the former has a much smaller role than the latter, with some even having him barely show up at all (The Time Trap for example only has him appear on panel in the very last page visiting Mortimer in the hospital).

Film

Turner of Turner And Hooch.
The film Music and Lyrics features an in-universe example: the lead character was part of an 80's pop duo named PoP!, heavily based off Wham!, with him playing the Andrew Ridgeley role.
Fanny in Fanny and Alexander.

Live Action TV

Travis Mayweather on Star Trek: Enterprise. Since TNG, Trek has always had a problem with its Cast Calculus. Tradition requires that there always be a Power Trio to mirror Kirk/Spock/Bones. Tradition also requires there always be a helmsman, a security chief, a fanservice character, an engineer, a doctor and ship's counselor on the show. Mayweather represents this contradiction at its apogee.
The Agony Booth: Oh, right�that's Travis Mayweather, the ship's helmsman. He gets zero lines in this episode. On this show, it's kind of a motif.
Parodied on That Mitchell and Webb Look with the superhero duo Angel Summoner & BMX Bandit. Angel Summoner is Exactly What It Says on the Tin, while BMX Bandit is good at riding a BMX.
Mindy of Mork and Mindy.
Greg of Dharma And Greg
Compared to the other six main characters (and even some of the recurring guest characters), Shirley in Community seems to receive comparatively little focus and attention.
In-Universe example, the plot of one Columbo episode involves one member of a writing partnership killing off the other - because he threatened to expose the fact that his partner did not do any of the actual writing.
Sometimes happens in Super Sentai and Power Rangers where the Sixth Ranger will be introduced to be as powerful as, or even more powerful, than the hero; but after his introductory arc tends to be increasingly sidelined. This is known in the fandom as "Sixth Ranger Syndrome."
- Also, sometimes, the Red Ranger is given so much plot focus, Mid Season Upgrades, and screentime that you get a Kamen Rider series that has five other characters standing around just because it's habit. Rangers has an s, and sentai means "squad" or "task force," but in Mystic Force and Samurai/Shinkenger, it's as if nobody told that to The Powers That Be and everyone gets Sixth Ranger Syndrome, getting the spotlight in an early Filler episode or two but never being relevant again.
Greta on the TV version of How to Marry a Millionaire. When Lori Nelson complained about this, it essentially led to the fall of the series... and the rise of Barbara Eden, another cast member on the show.

Newspaper Comics

Rat claims he is going to do this to Pig in one edition of the comic strip Pearls Before Swine; in commentary in his treasuries, author Stephen Pastis jokingly/seriously asserts that he was the first person to have used the word "Garfunkel" as a verb.
Anyone remember the last time Barney Google actually appeared in Barney Google & Snuffy Smith? Heck, the average Troper probably wasn't even born yet.

Tabletop Games

Magic: The Gathering players have a tradition of saying there are four colors: White, blue, black, and red. This isn't to say that green hasn't had some good cards; in fact, the Vintage restricted list has three green cards from the original base set on it. It's just that green has a bad history with this.

TV Tropes

Television Tropes & Idioms.

Video Games

Despite the name, the Super Mario Bros. games rarely give the two brothers equal billing. In games when Luigi is as important as Mario, both characters are mentioned by name in the title (e.g. Mario & Luigi: Superstar Saga). And you have all the characters in game who refer to poor Luigi as "that green mustache guy", somewhat verifying the trope in-universe.
There were two pack-in games that came with the NES. One was Super Mario Bros., of course. The other? Duck Hunt, which is remembered for only two things: Being the other game that came with the NES, and... the dog. Speaking of the NES accessories in order of well-known-ness: Control Pad, Zapper, Power Pad, Power Glove, NES Advantage, Robotic Operating Buddy.
- When I got my NES, it came with a three-game multipack, providing for an even lesser Lesser Star. Super Mario Bros. and Duck Hunt were the first two on the cartridge. World Class Track Meet was the third, a rereleased version of Stadium Events. Stadium Events is known for being the game that holds the world record for highest price sold for a video game (an eBay auction fetched $41,300 for a factory-sealed copy). World Class Track Meet, more widely released, is known for being 'that game you can totally cheat at if you step off the Power Pad and slap the pads with your hands'.
Same with Bob (blun/by) (the blue bubble dragon) from Bubble Bobble who has not been in as many games and ports as his brother Bub (the green bubble dragon) had. Coincidence?
Ratchet & Clank played with this trope in an interesting way: while in the early series Ratchet is undoubtedly the main character and Clank the sidekick, at the start the third game Clank is famous galaxy wide for his "Secret Agent Clank" holovid series while Ratchet (who plays his hapless valet) has faded into obscurity. Since then, they've been getting progressively more equal billing, with Clank getting more substantial solo gameplay portions as well as his own spinoff game...based on the aforementioned secret agent persona.

Western Animation

Parodied, of course, on The Simpsons episode "Lisa's Rival". Lisa takes solace in that there's nothing wrong being the second-best at anything. She then imagines a future in which she, Art Garfunkel, Jim Messina, and John Oates play their #2 song "Born To Be Runners Up". The concert is sponsored by (#2 car rental company) Avis. They get booed off the stage, and she wakes up lampshading the Fridge Logic of why people would show up to their concert just to boo them.
Metalocalypse:
- An in-universe example, the bassist Murderface is definitely considered a main character and major player in the band Dethklok. However, numerous episodes have shown that 1) he sucks at playing bass, 2) all the bass parts are written by lead guitarist Skwisgaar, 3) the bass parts are usually mixed to near-inaudible levels on the albums, and 4) in one in-character interview in a magazine, lead singer Nathan Explosion said that Murderface's duties in the recording studio are to simply play every single note one time, which is then laboriously assembled with Pro Tools into actual basslines one note at a time.
  - Murderface is shown in an episode to contribute to the band with dickish behavior. In the absence of his negativity, Dethklok loses its brutal edge.
  - When Murderface records solo singing parts for Planet Piss, producer Dick Knubler (who describes him as "almost part of Dethklok") can be seen actively brickwalling the sound montage to drown out his voice.
- Similarly, rhythm guitarist Toki Wartooth also has no input into the band's creative process. His parts on the album are written AND performed by Skwisgaar.
In the Family Guy episode "The Big Bang Theory", when Stewie's time machine whisks him and Brian out of the space-time continuum, he releases the machine's energy and as it turns out created the universe. When Brian attempts to get some of the credit from Stewie, he tells Brian that he's the "Art Garfunkel" of the universe.
Dale Armatre from Moral Orel. When his band, The Crucifolk, break up, its other two members(Who happen to be married) leave him out to dry, and reduced to doing middle school plays.