Lampshaded to some extent in the Adventure Game where while Cornfed does make a plan for Duckman to save the day, he decides that this time he needs to learn how to do things himself and doesn't help him directly outside of that.
Itchy Itchiford, (Itchy for short) from All Dogs Go to Heaven has this in spades, especially in the first movie and more so in the TV series. Charlie usually doesn't follow the phrase "think before you do" very well. Itchy prevents Charlie from going too far with his intentions for the most part, but even if he is unsuccessful in doing so, he always knows what is going to happen. Also, in the first movie, Itchy built Charlie's new casino.
South Park has "Coon and Friends", the pairing of Eric Cartman as the "hero" and C'thulu as his erstwhile companion.
Moreover, Penny's dog, Brain, is Penny's hypercompetent sidekick.
Although given Penny's competence, he's probably more her Puss (or should that be Pup?) in Boots...
In a similar vein, Spot from Hong Kong Phooey. There are two ways Hong Kong Phooey defeats a villain. Either by luck (when he's alone), or by his cat sidekick, who usually takes advantage of the villain being distracted by the hero screwing up.
Stan is Xander Crews' hypercompetent sidekick in Frisky Dingo. Likewise, Sin is Killface's.
The Simpsons: Although Mr. Burns is not incompetent so much as out of touch with the times, Waylon Smithers arguably serves this role.
Parodied in "Simpson and Delilah" when Homer is briefly made an executive at the nuclear power plant. His secretary Karl (asopposedto Carl) immediately realises that Homer is just some lucky buffoon and isn't suited to his new job. He proceeds to help Homer act the part, resolving every problem in Homer's professional and personal life without so much as being asked. He later gets fired protecting Homer's job and still writes a presentation to aid him. Homer does brilliantly even without him, but because he's bald again no one takes him seriously.
Jazz to Sentinel Prime in Transformers Animated. While Sentinel Prime is technically second in command to Ultra Magnus, Jazz is usually the one who keeps a handle on Sentinel and tries to steer him towards good judgment. Jazz eventually realized this was a lost cause and left to join the Autobots on Earth.
This holds especially true in the seriesDuck Dodgers, where Dodgers doesn't so much hold the Idiot Ball as have it surgically implanted in place of his actual brain. Apparently, the Cadet is so competent that he singlehandedly cured world hunger in his younger days.
Humorously, Plucky himself has once has served this role to Daffy in a Duck Dodgers short where he was "the eager young space cadet." Somewhat odd, since Plucky is a child version of Daffy and normally suffers the same defeat-by-hubris role that Daffy does.
This situation was reversed for Hampton and Plucky all of once. In the movie special, How I Spent My Summer Vacation, the Pig family picks up a hitchhiker - who turns out to be a (and this is quoted directly from the radio report that only Plucky seemed to note the importance of) "mass-murderer with a psychotic aversion to pork." Said "hitchhiker" then expanded his range of targets later as he pulled out a hockey mask and chainsaw and proclaimed, "I hate duck, too!" Insanity then Ensued.
Kif Kroker from Futurama is often shown to be far more intelligent and quick-witted than his boss, Zapp Brannigan, but on the rare occasions that Kif overcomes his shyness to speak up, Brannigan invariably ignores him, and often later blames Kif for his own mistakes.
"Be prepared to take the blame in three, two, one...Now!"
Shego from Kim Possible. She fights all the battles for Dr. Drakken, she tries to keep his evil plans in line, she even provides Drakken with the Unobtainium / Applied Phlebotinum needed for his capers (either by stealing them, or actually buying them). Add her being Dangerously Genre Savvy to the list, and the reason why she isn't the Big Bad instead comes down to pure lack of motivation. Shego is by far the best example of this on the show, particularly later on as Drakken became more and more silly and she became more clearly the only reason he gets anything done at all.
It should also be mentioned that the one time she did a caper on her own, during A Sitch in Time, she actually took over the world. But even then, she had to be talked into it by her future self.
Team Pet Rufus is often this to Ron, sometimes appearing to be smarter than his owner and much more mechanically adept. Many times has the day has been saved by Rufus running off and interfering on his own while Kim and Ron keep the villains busy. Lampshaded in "The Ron Factor."
Depending on the episode Ron himself may occasionally approach this, though as KP is barely ever inept and his moments tend to be one-offs he never actually makes it. "Roachie" is a fairly decent example.
Wade also qualifies; there are a few times where even Kim would be lost without him.
Interpoll the pet parrot from "Victor & Hugo -Bunglers in Crime" seems to be a lot smarter than his owners. Mind you, that's not saying much.
Peter Puppy from the Earthworm Jim cartoon was like this at times. In fact, because of this one episode featured a council of superheroes that ordered Jim to hand over his super suit to Peter, who at the end gave it back.
Charles Foster Ofdensen in Metalocalypse. Clever, take-charge, and literally DEADLY CFO, manager, and laywer who has more brainpower in one pinky than his metalhead employers have between them.
Proven after he died, when their wild, compulsive spending sprees and horrible business practices pretty much drive them to bankruptcy.
The answer is obviously Zuko. The real question is why hasn't she done that already?
And the answer to that is that for all her cunning, Azula is at heart an emotionally unstable wreck who needs Daddy's approval - when she loses it (or thinks she does), things turn nasty for herreal quick...
Also, Ty Lee for Azula. Ty Lee has the highest KO count in the series, because her fighting style is largely nonlethal and her victims recover pretty quickly. The other two-thirds of the Quirky Miniboss Squad, Azula and Mai, can't take anyone out without burning/electrocuting/stabbing them, which they really can't show on what is nominally a kids' show.
Iroh serves as this for Zuko in season one. He's arguably one of the most formidable characters in the series but is content to sip tea and give Zuko advice.
Arthur of The Tick is many times more intelligent than his partner, The Tick, but he's got nowhere near the combat prowess (or Nigh-Invulnerability) of him, so he's content to play second fiddle to the big blue superhero as it allows him to help people superhero-style while avoiding the punishment.
Confirmed. It was the very first El Kabong cartoon where the villain, Don Chilada, had El Kabong's guitar (which he uses to bash villains on the head) while the hero was incapacitated, but Baba Looey was inside the guitar and put a gun to Don Chilada's noggin.
Slinkman of Camp Lazlo is this to Scoutmaster Lumpus. When Lumpus isn't being a mad dictator, he's lying in a lawn chair making Slinkman do all the work. As Lumpus deteriorated, Slinkman gained more control over camp. Slinkman secretly dreams of being scoutmaster, but by the time the show ends, he pretty much is already.
Owen Burnett alias Puck from Gargoyles shows how dangerous one of these is when paired with a boss who's already a Magnificent Bastard in his own right (enough of one to get a couple of tropes named for him!). It's not that Owen is the smarter of the two, but that they're smart in different ways- Xanatos is a truly brilliant schemer, but it's Owen's cool efficiency and eye for details that make sure all the bases are covered, while occasionally acting as Xanatos's conscience. Both parties have genuine liking and respect for each other, and it's heavily implied that neither would be quite sure what they'd do without the other.
For the record, in "The Gathering: Part II", Puck mentions that he offered Xanatos the choice between a lifetime of loyal service form Owen or granting one no-fingers-crossed wish. Xanatos is smart enough to know the better choice.
And Puck respects him for that. Though one wonders if Xanatos decided to be cute about it and wish for Owen as his permanent sidekick.
And of course Preston Vogel is exactly the same way for Fox' father - without the aid of also being a magical being.
While he's supposedly more of a partner instead of a sidekick, Phineas and Ferb's Ferb fits this trope pretty well. Phineas is the idea guy and the spokesman of the two, but Ferb tends to have more mechanical expertise. He does most of the work building all their crazy contraptions and does all the menial jobs. He doesn't seem to mind, though.
Even more so in the episode where he's helping his crush Vanessa Doofenshmirtz get a component for her supervillain father. She shows herself to be somewhat resourceful and very agile, but Ferb shows that his capability dwarfs that of everyone except Perry.
Speaking of, Agent P. Major Monogram and Carl tend to spend much of their screentime goofing off and generally just being Those Two Guys, leaving Perry to stop Doofenshmirtz's plans with pretty much no help. Half the time, they don't even give him the slightest bit of information to go on, simply telling him to "Go find Doofenshmirtz and stop him"; this tendency is lampshaded when Perry has to work with a (human) British spy.
Agent Double 0-0: What, that's it? No files, no location, no contact; what kind of a mission is this?
GIR from Invader Zim is far more competent than Zim himself... but only in duty mode. Which only lasts a few seconds.
An example of how much more competent GIR is, is when Zim decides to lock GIR in duty mode. GIR captures humans, absorbs huge amounts of knowledge, and determines Zim to be the reason that they haven't taken over the planet yet.
Haroud serves this function (and combines it with Deadpan Snarker as usual) for Abis Mal in Aladdin: The Series. A classic example of this is Abis Mal explaining (for exposition) his plan to attack the heroes. Haroud politely replies "I know what the plan is, master. Why are you telling me this?"
It may be the case in the space-themed episode "Space Madness" of The Ren & Stimpy Show, where the titular duo's space counterparts, Commander Hoek and Cadet Stimpy, are sent to a mission that is roughly said to take around 36 years. They are exposed to the effects of the space madness, but Ren is the only one to succumb to them, while Stimpy does his job as The Caretaker for him in an unusually competent manner (in most episodes Stimpy's actions are well-intentioned yet careless). However, Stimpy might have been immune to the effects of the space madness due to being too stupid for them to have any effect on him, while Ren is mentally unstable by nature.
Spike is this for Twilight Sparkle in My Little Pony: Friendship Is Magic. While Twilight herself is generally pretty damn competent the number of skills Spike possesses is simply staggering and there are a few episodes where Twilight would have been completely screwed without him.
Generally speaking, the cartoons of the late 70's and early 80's each seemed to have their protagonists be best friends with an irritatingly cuteFairy Companion who could pretty much do anything the plot required. The most bizarre/notorious example would be Rubik, the Amazing Cube, which is pretty much exactly what it sounds like: the adventures of some kids and their magical talking, er, Rubik's Cube. Yes, as in the little cube-shaped puzzle where you match all the colors on each side. Really.
The only reason Rubik was a sidekick at all is that he could only walk/talk/save the day after he had been "solved", and the young boy he hung around with had the amazing ability to solve him quickly. So every episode Rubik had to be dropped or something, which was apparently enough to mix him up so that he couldn't fix everything in the first two minutes.
The Cartoon Network series Robot Boy revolves around Tommy, a short wimp with a giant head, who has been given the good Professor Mushimo's titular robot, whom the evil Dr. Kamikaze is determined to steal and use for evilness... Nessness. Tommy's task is to help Robot Boy become a real boy, while in the process Robot Boy continually saves Tommy and his friends from certain doom by means of unorthodox evil plan.
Since the show is named after Robotboy, Tommy is probably meant to be Robotboy's sidekick, not vice versa.
This is where we mention Glomer in It's Punky Brewster. Often cited as even more annoyingly ex Machina-y than most of these.
In Hanna-Barbera's The Godzilla Power Hour, poor Godzooky gets a lot of grief from fans because he's cute and much tinier than Godzilla. But taken objectively, Zooky is still a twelve-foot tall flying monster who dwarfs the human castmembers, and can handily intimidate humans who aren't expecting him. Apart from being a standard cute cartoon sidekick, he's also there so that even the human-scale filler scenes all Dai Kaiju stories have can still have a cool big monster in them.
Mr. Bogus's cousin, Brattus, often fills this role during very many of Bogus's adventures.
Soundwave of the Decepticons is probably the only reason the faction keeps running. He's the only one of Megatron's lieutenants who lacks Chronic Backstabbing Disorder, his skillset is extremely varied from being a capable spy and intelligence officer to a powerful warrior, and he has his own platoon of casseticons who alone can potentially be more useful than a lot of the full sized Decepticons.
Edd is this to Eddy on Ed, Edd n Eddy, much to Eddy's chargin. Ed will randomly be this for noth of them at random moments thanks to Rule of Funny.