A frequent occurrence in Prussia/the German Empire from 1812-1918. Field commands were traditionally given to high-ranking nobles, who were raised for the task but nevertheless had varying levels of competence. After Prussia's crushing defeat to Napoleon at the Battle of Jena (1806), Gerhard von Scharnhorst was put in charge of reforming the Prussian military, and came up with the idea of retaining the contemporary social structure, while cleverly undermining it by forcing the Field Marshals to co-operate with their Chiefs of Staff, who were appointed on Scharnhorst's advice. The most notable example of this was Field Marshall Paul von Hindenburg, who became a national hero and public icon during World War I, even though most of his decisions were made by the obscure no-name Erich Ludendorff.
In practice, Hindenburg had never been a very competent officer, and he had already been retired in 1911. The master strategist behind him and true brain behind the victory at Tannenberg was Colonel (future General) Max Hoffmann. Both had been decorated for the battle, Hoffmann promoted to General and Chief of Staff for Eastern Front Armies, yet the propaganda system gave the full credit to the old Prussian General and turned him into a national hero.
As the chief of staff in the Eastern Front, Hoffmann would pull off another one, masterminding the defeat (and collapse) of the Russian Empire while Prince Leopold of Bavaria was nominally in charge.
What Scharnhorst wanted to counteract most was the fact that especially in an army that went to war as infrequently as the Prussian one, high command tended to go to long-serving officers who had proved their bravery and gained some merit and done nothing wrong so bad to diminish their claim to command by virtue of their accumulated seniority. The system also allowed the commander and his chief of staff to complement each other. For instance in the Wars of Liberation General (later Field Marshal) Gehard Leberecht von Blücher supplied the more flashy courage, charisma and a natural talent to hold impromptu speeches to inspire his subordinates - including non-Prussian ones - with the strategic, tactical and administrative know-how of his chiefs of staff Scharnhorst and August Neithard von Gneisenau. There also was an interesting, effective synergy between the impulsive and audacious Blücher (it was an important factor that he was one of the few allied Generals who was not scared of Napoleon) and his somewhat more cautious chiefs of staff.
Another notable case was Helmuth von Moltke, the Prussian Chief of General Staff in the wars against Austria (1866) and France (1870-1871), when the (nominal) commander-in-chief was Wilhelm I of Prussia. In fact, a number of pundits and experts (including Friedrich Engels) had tipped the Austrians as most likely to win the war of 1866 because the Prussian army was led in the field by its uninspiring and militarily unremarkable king, while the Austrian was led by a general of proven worth. (Another factor that led people to fatally underestimate the Prussian high command was Moltke's age - he was born in 1800).
Much the same in Russian Empire also. The nominal commanders-in-chief was either the Tsar himself or one of his close relatives (e.g. Grand Duke Nicholas, a cousin of the Tsar Nicholas II, at the beginning of World War I). The trouble is that Russians often did not have a competent general who would act as the de facto commander. (Soviet Union continued this trend during World War II: Stalin (at least in the latter half of the war, when the Soviets were really winning) was the nominal commander-in-chief. The actual military command was exercised by Zhukov, as the Chief of General Staff.)
Ivan Konev was in turn Zhukov's Hypercompetent Sidekick, being just as talented and more intimately involved with the actual fighting.
This happened a lot during the later parts of the Roman Empire, especially in the 5th Century West, where ineffectual emperors were backed by military strongmen. Not all of them were constructive, but a few of them pretty much kept the West from falling apart immediately, most notably Aetius and Stilicho. Their deaths didn't bode well for Rome. Even the East had this. Belisarius was the famed general of Justinian and a fantastic commander.
Claudius was this to Caligula. At least for the first six months, when Caligula was sane. The jury's still out on after that; but it was only by accident that Claudius became emperor at all.
Marcus Vipsanius Agrippa was this for Octavian, later Emperor Augustus. While Octavian was a highly competent administrator, he needed someone who could match wits with Mark Antony on the battlefield and come out on top. That was Agrippa. He managed to absolutely crush not only the remnants of the conservative resistance to the Second Triumvirate, but also obliterate Antony's forces both at sea and on land. It is widely accepted that Octavian may never have become emperor if he did not have Agrippa handling the military side of things.
In a rather vile example of this; Heinrich Himmler (himself the pretty incompetent sidekick to Adolf Hitler), the man who supposedly carried out the Holocaust, had Reinhard Heydrich who carried out and created many of the ideas of the Holocaust. He was so vicious, it is said some of the Nazi officials who were his subordinates were more afraid of him than Hitler. This makes sense, as he created the concentration camps and the rest of the Final Solution.
Hitler had several of these, something which was not hard to accomplish. The most notable examples would be Erich von Manstein, Erwin Rommel, and Gerd von Rundstedt.
Vice President Walter Mondale was this to Jimmy Carter, serving as Carter's troubleshooter (particularly in foreign affairs).note Mondale's foreign affairs experience later earned him an appointment as ambassador to Japan under the Clinton administration.Richard Nixon filled the same role for Eisenhower. Prior to Mondale and Nixon the vice-presidency was little more than a ceremonial posting, and usually a dead end for a political career.
Sherpas for mountaineers, especially Tenzing Norgay for Sir Edmund Hillary, as noted elsewhere. Small subversion in that Norgay DID become famous, and Hillary gave him all possible credit.
It's worth noting that the famous photograph from the summit of Mt. Everest is, in fact, a photo of Norgay since Hillary was the only one who knew how to operate the camera, and standing on a mountain peak at 29,000 feet is not the time or place to try and give photography lessons.
This can occur with examples of Ass in Ambassador, since (in the case of the United States) the actual ambassadors to friendly countries like France and England are given the jobs as political favors by the president, while the actual nitty-gritty day-to-day running of the embassies/consulates/what have you are done by career Foreign Service Officers. The career FSOs, i.e. the ones who've made a long life out of doing the job, are often considered equivalent to high-ranking military officers in terms of authority and expertise.
Pretty much the entire civil service in the United States operates this way: agencies and departments are nominally run by political appointees but the day-to-day work is done by career professionals, some of whom have served through multiple administrations and even more appointees.
Australian deputy Prime Minister Paul Keating was arguably this to Prime Minister Bob Hawke. Despite bring a high school drop out, he was the architect of far reaching economic reforms that changed the entire way the economy functioned. He did all this while the Rhodes scholar Hawke acted as the lovable, yard glass chugging head of the Labor party.
To a degree, Stonewall Jackson, James Longstreet, and J. E. B. Stuart were this to Robert E. Lee. Lee was certainly no slouch, but at Gettysburg, with Jackson dead and Longstreet at odds with him, Lee made some major tactical blunders that are often interpreted as his having become dependent on a team of Hyper Competent Sidekicks he could trust with the details of carrying out his orders.