Plot Irrelevant Villain

Here we have Joe. Joe frequently appears throughout the narrative to do what he can to make Frank's life miserable.

The problem? Joe isn't actually essential to the narrative and isn't particularly interesting, either. Where a serious villain would Kick the Dog to inspire an emotional reaction, this guy barely manages to Poke the Poodle. He'll dash onscreen every so often, twirl his moustache in a Jerkass manner, and then leave with little fanfare.

In other words, Joe is a villain who doesn't do anything. He has been shoehorned into the narrative for little reason beside the conventional wisdom that all narratives need a clear bad guy. For this reason, he's an especially common addition to adaptations intended to reach a wider audience than in his original form.

While the easiest way to sum up this trope is "useless character", the phrase "Plot Irrelevant Villain" is a more objective descriptor as to what's going on. For example, Oogie Boogie from The Nightmare Before Christmas, awesome though he may be, is motivated purely by For the Evulz, causes trouble only after the Denouement, and has little if anything to do with the main plot of how Halloweentown takes over Christmas.

This trope can possibly go in line with Designated Villain. If he's there to provide someone to boo because the main villain is either too cool to hate or else morally neutral/abstract (e.g., a runaway train, an earthquake), it's a Hate Sink. Compare with Breakout Villain and Orcus on His Throne. When it's an entire unwholesome class of characters who don't seem to do any of the dirty deeds of their profession, it's The Pirates Who Don't Do Anything.

Examples of Plot Irrelevant Villain include:

Anime and Manga

From Pokémon, Gary Oak in the first season. He's a Jerkass that continually antagonizes Ash Ketchum solely to reinforce that he's better at everything - this only factors passively into Ash's motivation to become a Pokemon League Champion.
- Team Rocket also fall into this sometimes, mostly in the movies where they sometimes only show up to keep up appearances.
In the first season of Yu-Gi-Oh! 5D's, there was Devack, one of the Dark Signers; while most members of this group had extensive backgrounds, motivations, and some sort of connection to the heroes, Devack had none whatsoever in all three areas. He was a Card-Carrying Villain who seemed to despise the Signers for no known reason. (The Yu-Gi-Oh! 10th Anniversary Animation Book explains that Devack was originally intended to be from a demon worshipping cult and was sacrificed to the Earthbound Gods, but then reborn as a Dark Signer.)
One Piece had Wapol, the closest thing to a Big Bad in the Drum Island Arc. While this guy had a cool Devil Fruit power with the potential to make him a threat, he was never even a small threat to the heroes, he was just... there, and the arc would have gone smoother had he not been there. Ironically, he became a rather complex and interesting character after he quit being a villain and went into toymaking.
In Wizard's Soul - Koi no Seisen, the Alpha Bitch and her two lackies try to sabatoge Monika's chance at victory in the TCG tournament by doing things like file Monika's card sleeves so it looks like Monika's a cheater.
Sword Art Online has an odd in-universe example: the Big Bad and Final Boss of the Fictional Video Game was originally a demon (for lack of a better term) called An Incarnation of the Radius, which was to be fought at the summit of the giant tower of Aincrad - the tower's full name is "Aincrad, an Incarnating Radius", making this Boss a personification of the tower itself. However, when Kayaba Akihiko (the Big Bad of the original series and the game's in-universe designer) turned SAO into a Deadly Game, he replaced the Final Boss with an avatar of himself as the Final Boss. (Word of God states that Kayaba believed he had made the monster too strong and that no players would ever defeat it; while he had no concern for their lives, his ultimate goal required someone to eventually defeat the final boss.
- The villain in the full-length movie Sword Art Online The Movie -Ordinal Scale- discovers this unused Boss through data mining, figured it was a shame to waste it, and used it as a weapon against the heroes, resulting in an epic battle where every survivor from the original series squared off against the boss-who-never-was.

Film

In the movie Fired Up, the stereotypical evil cheerleader captain of the Opposing Sports Team is introduced as a big villain... and does nothing in her five minutes total screen time other than badmouth the good team a couple of times, and have sex with the female lead's Jerkass boyfriend. The audience knows he's sleeping around, so this role could be filled by any random girl).
The rival climatologist team in Twister subverts this - they seem entirely redundant, and Jonas Miller seems to be there just to make some anvilicious anticorporate points, but it's Dr. Miller's (attempted) theft of the Dorothy concept and Dr. Harding's anger at it that ultimately pulls him back into the stormchasing team.
The film Recipe for a Perfect Christmas had an office rival for the heroine who did not directly harm the heroine at all but still gets a verbal slapdown for offering her own ideas to the boss while the heroine has been suspended from her job.
Although he's a very memorable character, pretty much the entire plot of The Nightmare Before Christmas happens without Oogie Boogie, and the Final Battle happens after the climax as a way of tying off loose ends rather than causing any resolution or character development.
- Tellingly, in the original poem (found on the blu-ray narrated by Christopher Lee) Oogie Boogie doesn't appear at all despite the rest of the poem following the movie point to point.
Humma Kavula from the The Hitchhikers Guide to The Galaxy movie. Oh yes. He's given little Backstory, his motives are only hinted at, and seems to exist only to push for the inclusion of the MacGuffin used to save the day at the end. No doubt if sequels were made he'd have a larger role, but sequels seem unlikely at this point. And the most aggravating point is that the movie already had villains! Do the Vogons chasing Zaphod for kidnapping the President (himself) and stealing a ship not count?
Gigantic is an indie romantic comedy. Not exactly a genre needing a villain, yet for some reason it has a strange homeless man who attacks the male lead at random intervals for basically no reason whatsoever. One of the more bizarre examples, as there is not even a token attempt to shoehorn him into the plot, he's just there.
The closest Madagascar has to a villain are the fossa - but they are a menace that hardly appears. The major conflict is both the protagonists being stranded in a strange place, and the sole carnivore of them becoming hungry.
"Leo" (aka "Crater Face") in Grease. A pretty generic punk, there really wasn't much to distinguish this guy from the other Scorpions, or even most of the T-Birds, so it was never necessary to single him out at all.
- In Grease 2 he reappears, is given a last name ("Balmudo"), and seems to be just as irrelevant to the overall plot -- until he leads his biker gang in an attack on the senior luau at the end of the movie.
Pyramid Head in Silent Hill. Now, in the video game Silent Hill 2, he was very relevant to the plot, being the embodiment of the James' guilt over his past and desire to be punished, existing to remind him of it and preserve his humanity. However, neither James nor any similar character exists in the movie, so Pyramid Head (referred to as Red Pyramid, though it's obvious who he is) makes very little sense in this adaptation.

Literature

Draco Malfoy is this most of the time in the early Harry Potter books. He only really starts to dovetail with the actual villains in book five.

Live-Action TV

The insane simulant in the Red Dwarf episode 'Justice': Aside from providing an excuse for reaching the space station, he had no purpose other than to tack on an (admittedly funny) action sequence after the plot proper was resolved.
- The simulants are perfect for this sort of thing: Need to get the crew in a Wild West simulation? Simulant. Need a reason to get Rimmer on his own planet for 600 years? Simulant. Need a way to introduce a drugged-up twin brother of Kryten? Simulant. The only Simulant that appears that is directly related to the plot of the episode is The Inquisitor, and really, he might as well not be one, as his motivation isn't the killing of humans, but replacing them in history with those he thinks deserves life more.
Kamen Rider Den-O worked well as an ensemble Monster of the Week show, and then basically fell apart at the very end, when they tried to introduce a primary antagonist. Not helped by the villain's motivation being rather obtuse up through the end of the series.
This applies to most movies made by the SciFi/SyFy Channel. You have a decent monster/phenomenon story, then you throw a bunch of criminals in. Maybe they are trying to get us to root for the monster, or increase the body count without angst (because the extra victims are bad people, and they have it coming), but it usually just muddies up the movie.
The Jabberwock in the 1985 Irwin Allen version of Alice in Wonderland is an unnecessary addition to the 'Through the Looking Glass' portion of the film. In the original book, the Jabberwock never appeared outside the poem "Jabberwocky". Irwin Allen, however, believed the story needed an equivalent to the Boogeyman, so he made the Jabberwock appear and scare Alice when she reads the poem, and then turn up again twice later (once at the end of the Humpty Dumpty scene, the second during the climax). But really it contributes nothing to the story, aside from allowing the producers to put in a climax somewhat more comprehensable than the book's rather bewildering finale.

Tabletop Games

Initially Candy Land had no villain or even much of a plot, but an updated version added Lord Licorice, whose scheme involves turning all the candy in Candy Land into licorice - but he's a clumsy fool who is easily sidetracked. Not much more than that.

Toys

The Incredible Crash Dummies was a line of toys that really didn't need a villain because it really didn't have a plot, just a bunch of dummies in toy vehicles that were fun to crash. But in an effort to expand the line, they introduced Junk Man, a Card-Carrying Villain with no point whatsoever. The commercial even lampshades this, with the narrator screaming, "The Crash Dummies lives will never be the same!" (Car crashes.) "Well, almost never."

Video Games

Midboss from Disgaea: Laharl even named him Midboss because he was a seemingly unimportant villain, and he continually returns to antagonize Laharl's troupe for no apparent real reason. Subverted when it's reveled that he was helping the seraph's Batman Gambit by monitoring Laharl and co. to make sure everything was going according to plan.
In the Spider-Man games, Shocker qualifies. Almost every other villain has an important role in the story to some extent. Shocker is just there to get his ass whupped and not make a single contribution to the story.
Zed from Wild ARMs might qualify, too.
To an extent, Batman: Arkham Asylum has Bane: he shows up once to fight Batman and gets taken down immediately, unlike the other villains who all come back at least once. His indirect role in the plot, however, is much greater: Joker plans to use a deriative of the Venom formula in his blood to make rampaging monsters out of all of Gotham.
Bowser becomes this in Paper Mario: The Thousand-Year Door. All the scenes involving him most;y involve him moping about - and emphasizing the fact that - someone else has nabbed Peach and that someone has usurped the role of Big Bad from him. While he does have a memorable scene as the penultimate Boss (mostly to prove that, above all, he's the biggest bad guy of the franchise) in the end, his involvement accomplishes nothing whatsoever.
The Great Mighty Poo from Conker's Bad Fur Day. Sure, he's the most Crazy Awesome boss in the game, but he has nothing to do with the main plot.

Western Animation

The main antagonists, Duchess and Terrence, from Foster's Home for Imaginary Friends, were important in the pilot and pretty well ignored since. The show never really needed bad guys, and when it did, it could usually be better performed by Bloo, the resident Jerkass.
The Christmas Special Christopher the Christmas Tree has a scene where a fox and weasel show up for no reason other than to lend the end of the special a little suspense by planting the idea that Christopher will be chopped down for firewood, rather than picked to be a Christmas tree.
Transfer (and his boss, Sullivan) in Around the World with Willy Fog: Transfer sets up a lot of obstacles for the heroes, yes, but in the original book those obstacles arose just fine without anybody trying to sabotage the trip.
Parodied in the American Dad episode "Don't Look a Smith Horse in the Mouth", where Roger is riding Stan in a horse race (Stan's mind is temporarily in a horse's body). Roger mentions his regret that he doesn't have a rival to race against and make it more exciting, so when Stan points out that it isn't too late, Roger deliberately picks a fight with another jockey just to create a rival.
Peyo's original comic book version of The Smurfs story "The Astrosmurf" had No Antagonist; the cartoon adaptation, however, put Gargamel in it for some scenes, trailing the Smurfs with a crystal ball to give an added risk of Dreamy Smurf catching onto the plan; he was driven away quickly, and really wasn't necessary for the story as a whole.
The Big Bad in The Little Mermaid II: Return to the Sea is by Ursula's "crazy sister" Morgana, who wants to kidnap Ariel's daughter because... ah... well, cause she's evil. Maybe there was some suggestion it was over revenge, but to be frank, she was little more than a thinner version of Ursula. Rather than simply concoct some way for Ursula to have survived the first film, they came up with this entirely unnecessary sibling. But then, it wasn't a very good movie overall.
Ernie the Giant Chicken on Family Guy; the long, drawn-out fights between him and Peter are almost never relevant to the plot and done with Rule of Funny in mind.