Disney Comics have recurring stories featuring Sherlock Holmes parody "The Sleuth" with Mickey fulfilling the role of Watson. Seeing as The Sleuth seems to have the same investigative capabilities as Inspector Gadget, it's not hard to guess who fulfills this trope...
Iznogoud: Wa'at Alahf, Iznogoud's henchman. While he acts and looks dumb most of the time, he tends to have sudden Let's Get Dangerous! moments where he reveals he can be very competent when needed. He's also far more lucid than his master about the fact they can't win.
For Deadpool, it's Weasel and Al who play this role. Weasel does pretty much everything but the actual grunt work while Al tends to provide some helpful insight in between tormenting her captor by doing things like telling him the salt is sugar (which Pool then proceeds to heap on his cereal, making for a funny spit-take).
Poor, poor Arthur from The Tick. Then again, he might not be hypercompetent, just far more competent than his boss, which isn't exactlydifficult.
See also the animated version.
To those who don't know better, Lucius Fox is this to Bruce Wayne.
Alfred is often this to both Bruce Wayne and Batman. And most of the other members of the Batfamily too, Dick Grayson, Cassandra Cain, Tim Drake, Damian... they all turn to Alfred for help on not-so-rare occasions.
For a while, Green Lantern Alan Scott was sidekick to... a dogNote (Streak the Wonder Dog, not to be confused with Rex The Wonder Dog, though both were DC Comics characters, and Rex was largely based on the earlier canine star.)
Frank Miller's The Big Guy and Rusty the Boy Robot (later made into an animated series). The titular big guy was the result of research to create an autonomous robot to protect the USA against the USSR, however while the body was functional, no one could code a proper AI for it, and thus the government converted the big guy into a piloted robot, keeping the fact that it had a human pilot rather than an AI secret. Two decades later, the corporation that built the big guy has a break-through in AI research. The trick is however that the AI can only be coded to be of a similar mentality as a child, and that it needs to learn like a child to that it can grow into the adult, soldier-like mind the US government wants. Equipped with energy weapons, Rusty, the boy robot, is paired with The Big Guy (whom he is led to believe to be a real robot, so that Rusty will try to emulate him and model himself on him). Thing is, despite being an eighth of the big guy's size, Rusty has more firepower than the big guy, only his immaturity keeps him in line and acting as sidekick to the Big Guy, whom he's supposed to replace eventually. Really, the theme song says it all.
Johnny Thunder was like this, being in possession of a basically omnipotent genie who will do whatever he says. Unfortunately, he can do only what Johnny says, and Johnny isn't the brightest guy around. His Legacy Character Jakeem Thunder is brighter (and Johnny himself has merged with the genie), but also thirteen years old and lacking in maturity.
In his earliest appearances, Johnny wasn't even aware of the genie. He'd accidentally say the magic phrase ("Cei U", pronounced like "say you") that summoned the mystic thunderbolt, and then whatever Johnny idly wished for ("I sure wish I could find a way to get over that fence") would mysteriously happen.
In a notable difference to other continuities where Robotnik surrounds himself with idiots and backstabbers, his right hand man in Sonic the Comic is his chief scientist Grimer, who is loyal, dedicated and professional. As well as being the primary designer of many of Robotnik's most dangerous war machines, he personally comes to Robotnik's rescue on several occasions. The only area Robotnik is more dangerous is direct combat being a Genius Bruiser where as Grimer is a Non-Action Guy and can't fight without machines. His finest moment came when he was jailed after Robotnik was apparently destroyed by the Chaos Emeralds, where he took control of his prison, hacked into the Kintobor computer to keep Sonic under absolute surveillance and ultimately outsmarted and outmaneuvered the heroes to find Robotnik.
In Sonic the Comic – Online! he chessmasters his way into discrediting Sonic, leaving Mobius to the mob, and starting a destructive chain reaction of volcanoes before escaping to another universe. He appears near the end to gloat to Sonic, as a hologram. Badass.
Since the whole point of the comic is about making him more competent, Paperinik, Donald Duck's superhero identity, is far from incapable. However One is a master hacker, can create incredible machines in little time and has knowledge about practically every subject. Both would probably be offended if you call the computer "sidekick", however: they are partners.
With Knight and Squire, the British equivalent to Batman and Robin, Squire (Beryl Hutchinson) is a more accomplished detective and organizer than her boss, Knight. More often than not, it's she who's saving him from danger, as seen in Batgirl Vol. 3 #22. Of course, Knight is pretty badass in his own right...
In Hawkeye, Clint Barton pretty much admits that his sidekick/partner Kate Bishop is the better Hawkeye of the two.
Boo of Copperhead thinks of himself as one, given that he served as interim sheriff before he was redemoted to deputy.