In Excel♥Saga all the girls Il Palazzo employs are flawed to some extent, but Excel is the one that is most likely going to mess up whatever new plan he has for taking over Fukuoka City. She is also completely delusional with regards to how much Il Palazzo cares about her.
By the third or fourth capture, Keima has acknowledged that his partner Elsie is basically completely useless. He points out that partners these days are supposed to be intelligent and capable, so she's all happy that she has Keima in that case... which gets her yelled at for thinking she's the main character.
In A Cruel God Reigns, Savage tends to fall into this category for Ian. He isn't dumb, persay, but he doesn't often think before acting, and he seems to often be swaying for his Even the Guys Want Him type love for Ian. He is very much a secondary, side-kick k character, and the two's interactions are usually played for laughs.
X-Men villain Toad was played this role for Magneto for a very long time. He didn't start to grow balls until the '90s, and even then, he was still the Butt Monkey until The Movie came out where — thanks to additional ranine abilities like a "nasty tongue" and spitting goo — he became quite an effective villain, which carried over into the comics.
Teen Titans: Bette Kane, a former member of the Teen Titans, and prior to some retconning the original Batgirl, has been portrayed as this for many years. Recently, she decided to come out of retirement while in college, only to end up being kidnapped and held hostage by a serial killer a mere issue after her initial decision.
From Lucky Luke, Averell Dalton for his brother Joe.
Generally speaking, if a Golden Age superhero didn't have a Kid Sidekick, he'd be saddled with one of these guys for "comic relief":
The fourth film replaces Otis with Lenny Luthor. Lex regards his teenage nephew as "the Dutch Elm disease in my family tree".
Dibbs, Carrigan Crittenden's henchman in the 1995 film Casper.
Annoying comic relief Bumbling Sidekicks were a staple of Masked Luchador films starring El Santo and other wrestlers. Just taking a look at one of them, Perico (from Santo en El Tesoro de Drácula), on this page's Image Links, should give you the general idea.
The burglar Marv in Home Alone 2. In the first film, he and his partner Harry appear to have a more equal relationship but in the second film he is clearly Harry's dragon and a lot dumber than he was in the first film. Also, Cedric the bellboy is the Bumbling Sidekick to Mr. Hector, the hotel concierge at the Plaza Hotel Kevin stays at.
As a teenager, Peter Pettigrew was the Bumbling Sidekick to the other Marauders in Harry Potter.
Stolen from Gypsies has two, both probably inspired by Baldrick from Black Adder. The protagonist/narrator has his servant Antonio, and in the story-within-a-story he's writing, there's the character Short Clog. Since the characters in the story-within-a-story reflect the narrator's life, it's likely Short Clog reflects Antonio, although the two are somewhat different- Antonio is a bit of a Hypercompetent Sidekick, whereas Short Clog is a straight up Bumbling Sidekick, being a dullard with bad hygiene.
Parodied in the Doctor Who Missing Adventures novel Managra, where the Bumbling Sidekick to the resident dashing hero is in fact a lot smarter than he lets on — and, indeed, a lot smarter than his boss in many ways — but pretends to be a dimwit because it pays better.
Agent Sydney Bristow to Agent Jack Baxter in The Ultra Violets. While one is a perfect fit for the job, the other couldn't be more out of place.
"Sod-off" Baldrick is a classic example, as well as the former Trope Namer. In the first season, he was a Hypercompetent Sidekick, but a Retool between seasons transformed him into the clumsy, clingy idiot who put up with a beating an episode. By the time of the fourth TV series, Blackadder Goes Forth, Private S. Baldrick's stupidity borders on insanity.
Series 1 and 2 had Lord Percy Percy, and Series 3 and 4 have George.
Manuel, of Fawlty Towers, is this. A Spaniard from Barcelona, Manuel's ineptitude for the English language combined with the neurotic Basil Fawlty's knack for causing chaos made him often cause things to go even worse. Basil firmly believes Manuel to be of subnormal intelligence.
Dwight from The Office (US), albeit only when he is accompanying his boss, Michael Scott.
In the UK comedy series The New Statesman, Piers Fletcher-Dervish is Alan B'Stard's long-and-brutally-suffering sidekick. Not really under any illusion that Alan likes him, but too terrified to end the relationship.
Ted from Scrubs. J.D. fits this trope when he's around Dr. Cox.
Star Trek: Voyager: Lonzak, the incompetent henchman of Dr Chaotica in the Captain Proton holoprogram.
Heroes: Sylar gains one in the form of the teenager Luke in Volume 4. Luke forces Sylar to not kill him by saying that he knows where Sylar's father is. However, Luke himself is a bit of an ass and really gets on Sylar's nerves. Once Sylar finally figures out where his father is, he ditches Luke and never looks back.
Merlin's interaction with Arthur often comes off as this in Merlin , even though sometimes he's pretending.
Arguably, Schultz from Hogan's Heroes, though he's probably actually not as bumbling as Col. Klink—Klink is at least trying to be competant, whereas Schultz often is deliberately oblivious to what Hogan's crew is up to.
In Molière's Don Juan, Juan's servant Sgnanarelle is pretty much this, a bumbling Dirty Coward who isn't treated very well by his master.
Poor little Pete from Bully kissed Gary's ass for God-knows-how-long until Jimmy saved him.
Elliot from Jagged Alliance 2 fits this like a glove. His boss, the very bitchy and hot-tempered Queen Deidranna enjoys killing the messenger. In this case, it's always Elliot, and it always involves her slapping the s*** out of him, and in one instance, shooting him from point-blank with a pistol... only to have him get up and insist that he clean the mess himself. He is incredibly devoted to her, regardless of the abuse he takes, and actually would survive until the end of the game if your mercs don't find him and put him out of his misery.
Mieu a.k.a. "Thing". He's a typical cutesy animal like you'd find in many a fantasy anime, complete with an annoying squeaky voice and Spoon Speak. What makes him a Bumbling Sidekick is his undying faith in his master, who gives him the aforementioned nickname, bashes him into a soldier's helmet to knock the soldier out, and every other time he speaks, he either kicks it around or tells it to shut up, or (usually) both.
Elan is often portrayed as Roy's Bumbling Sidekick. In the Origin of the PCsprequel, he definitely is toward his Paladin partner.
On the villains' side, Thog is this for Nale in the Linear Guild.
Greasy of the Whateley Universe, the deviser who's the sidekick of annoying horndog Peeper around the Whateley campus. Despite this, he's still more competent than Peeper himself (being a modestly skilled Devisor), but that's not saying much.
GIR, Invader Zim. Zim acts this way towards the Tallests, though he's clearly the protagonist.
Hesh from Sealab 2021 is considerably ruder and more self-assertive, but he still fits the pattern.
Meatwad from Aqua Teen Hunger Force acts like a small child, complete with imaginary friends. This lets him be the perfect Bumbling Sidekick — he's clingy, gullible, stubborn, useless in an emergency, and has no attention span. He also has the wild sidekick luck — his fortunes vary from being sold for cash to becoming the god of Christmas. The golf videogame lampshades this with comments like "What a rotten friend you are!" when describing the pickups allowing you to use him as a golf ball or as a distraction for the enemy to target.
Pinky from Pinky and the Brain is not desperate, nor does he ever quite demonstrate the delusion that he is appreciated. Rather, he is simply too scatterbrained and cheerfully oblivious to notice that such a thing as contempt exists, much less that the Brain harbors so endless a supply of it for him. Deep down, the Brain really does care for Pinky as much as Pinky, who considers the Brain his best friend in all the world, cares for the Brain.
Both Ed and Edd from Ed, Edd n Eddy take more than their fair share of abuse from Eddy (although in Edd's case its not stupidity that's the problem but instead being overly moral and verbose). Both however are likely to get Eddy into an unpleasant situation, usually by accident.
Harley Quinn from Batman: The Animated Series was this to The Joker. Admittedly, the Joker generally seemed to view her as his favorite henchman. Given that the Joker's favorite person is Batman, however, she still gets treated pretty badly.
Frizz and Nug are often this to Sgt Blob in The Dreamstone, if not all that willingly. While Blob himself is delusional enough for even them to have the occasional intellectual superiority to, they lack any sense of tactfulness, bravado, or even much evil ambition whatsoever, so much that if Blob didn't drag them into each mission they'd probably stay at home. Blob himself (along with Urpgor) are bumbling Mooks to Zordrak.