Intolerable Cruelty names this trope "The Tenzing Norgay", after the Sherpa who helped Edmund Hillary get to the top of Mount Everest.
Vadinho from Puma Man is a Badass Normal who constantly hand-holds the nominal superhero Tony through the adventure and displays power and badassery in such quantity that you wonder why he needs Tony at all.
Will: Do you hand [your Hero] A) his silver-tipped crossbow, B) a wooden stake, C)...
Zach: I'm already holding his crossbow, why can't I just shoot it myself?
A prevalent running gag in Big Trouble in Little China. Jack Burton acts like the hero, but it's his sidekick Wang who actually knows what's going on.
And yet it's Burton who kills the Big Bad by catching a knife thrown at him and "returning" it.
Nobody will ever really understand why Jules agrees to serve under Reynolds Pirates XXX.
Warriors of the Wasteland (aka 'The New Barbarians'): the bow-and-arrow-wielding Nadir does a better job of dealing with the homicidal Templars than the purported hero, Scorpion. He does it so well that it's usually his character depicted on the cover.
R2D2 in Star Wars, particularly if viewed as specifically C-3PO's sidekick. In the original trilogy, he hacks the Death Star main computer to show its internal lay-out and shut down the trash compactors, keeps Luke's X-wing flying, and functions as a spy and monitoring station. He's also shown a number of times to be particularly brave and determined. In the prequels, it's the same story again: repairing a ship in hard vacuum while other droids blow up around him, flying, and once again hacking in the enemy's flagship.
In the Expanded Universe Artoo continues this trend. He's effectively saved entire planets and civilizations of the Galaxy numerous times thanks to saving Han, Luke, Leia, or whoever the hell he's with repeatedly despite great personal risk to his tiny droid self. It's all the more impressive that he accomplishes this without really having any direct defenses of his own.
Of course, Word of God from Lucas himself has (sometimes) been that what we see aren't the true events, it's R2 telling the story to an alien race. It's entirely possible that he embellished a bit, especially since most of his biggest heroic moments had no organic witnesses.
Played straight from the point of view of the Watership Down rabbits in that Bigwig is tougher, stronger and more experienced in combat than Hazel, and in many warrens this would qualify him to be Chief, yet these rabbits have been through so much and come to respect Hazel's qualities of leadership, lateral thinking and delegation that he is, without having to even decide on it, the Chief. It's beautifully played with, though, when Bigwig faces down Woundwort at the end and informs him that his Chief told him to defend the run - Woundwort is visibly taken aback since he can't help but imagine the rabbit that could command Bigwig to be even stronger than him!
Played with in The Devil Wears Prada. On the one hand, Andy and Miranda's other employees are regularly expected to do the impossible instantly and perfectly. On the other hand, this is not because Miranda is a Fake Ultimate Hero; rather, she's The Ace and demands the same from everyone else. When Andy arrives for her interview during the fim's opening, she is informed that Miranda has burned through a long string of assistants because they were not hypercompetent enough.
In Iron Man, Tony Stark may be able to build a miniature arc reactor in a cave, with a box of scraps, but it is no secret that for all his genius, he can't function without his ever faithful assistant, the beleaguered Pepper Potts. To the point that Tony doesn't even hesitate in making her the CEO of Stark Industries during the first sequel, seeing as she's essentially been running the company for him for years.
Tank Girl. The title character is fairly competent on her own, but her sidekick Jet Girl is significantly saner and somewhat more practical, meaning that because of her most of Tank Girl's schemes don't end with her dead.
In One, Two, Three Schlemmer (Hanns Lothar) often is this to C. R. MacNamara (James Cagney), as he is the one who has to implement most of his zany schemes.
Notably, this was the original plan for Disney's Aladdin, where the Evil Vizier Jafar would have been a bumbling fool with his competent parrot sidekick Iago providing the real brains of the operation. Then they switched roles and look out.
Despite officially being Mortdecai's assistant, Jock is responsible for almost all the heavy lifting and at least half the brainwork of what they do.