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", that's more objective as what's going on here. 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 problem is too cool to hate or a morally neutral problem (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 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 antagonist to Ash for absolutely no reason, and continually antagonizes him in ways that never add anything to the story.
- Team Rocket also fall into this sometimes. Sometimes only showing up to keep up appearances.

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 (who the audience knows is sleeping around, so this role could be filled by any random girl).
The rival climatologist team in Twister is entirely redundant and has no useful role in the story.
- This is more of a subversion than a straight example. Jonas Miller seems to be there just to make some anvilicious anticorporate point, 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.

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 5.

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.

Western Animation

The main antagonists, Duchess and Terrence, from Fosters 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.

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.