Darth Sidious in Star Wars (as Chancellor Palpatine). Three years into the Clone Wars, the Republic was a military dictatorship in all but name, and Sidious had a supermajority in the Senate who did everything he said. Although his rise of power had been planned out in meticulous detail before anyone noticed him.
And his closest political allies knew he was a Sith Lord long before he made himself Emperor.
Daala is sickened by the ranks and self-promotions the warlords have invented and/or given themselves. This, combined with other reasons, results in Daala ending the Enemy Civil War and uniting the imperial military. , , , 
President Berzelius "Buzz" Windrip of Sinclaim Lewis' It Can't Happen Here, later adapted as V.
And by extension Charles Lindbergh as presented in Philip Roth's The Plot Against America (Roth's novel is a Spiritual Successor).
In Octavia Butler's Parable series, a dystopic United States elects Reverend Andrew Steele Jarrett, a radical preacher who eventually leads a crusade against all non-Christians and other undesirable groups, blaming them for the devastation of the economy and using them as a scapegoat to unite the people against.
Big Brother in 1984. Nobody has seen him in person, but his face is worshiped on posters and on the telescreens.
Christopher Goodman from Christ Clone.
Greg Stillson, the obscure up-and-coming local politician destined to become President and destroy humanity from Stephen King's The Dead Zone, certainly fits the "political outsider with bizarre behavior and no obvious qualifications who nonetheless manages to climb to power through populist rhetoric and spectacular publicity stunts" part of the trope. The narrator even outright says that Stillson is obviously unsuited for serious public office, but the voters enjoy his theatrics and vote him into power anyway as a sort of "screw you" to the Washington establishment, believing that he'll shake things up without doing any actual harm. This proves an exceptionally poor decision on the part of the voters, as while Stillson has no actual over-arcing Evil Plan, he's obviously loony, secretly corrupt, and criminally inclined, and the sort of person who would start an unnecessary nuclear war just because he felt like it (and eventually does).
The Anti Christ in Left Behind. Though his rise to power completely ignores the Rapture occuring less than two weeks ago and is even in complete contradiction to the supposed off screen record crime waves. He just becomes the head of the United Nations and says it would be nice if every nation would destroy or hand over all their weapons to him so there can be world peace. This works.
The Sword of Truth, given its Anvilicious libertarian themes, whenever an enemy is this, it instantly makes them an acceptable target for just about anything.
Jagang himself: he's essentially the product of magic in a society that hates and fears it, he snapped up almost all of the known world, and through exceedingly clever management, the ability to run a crowd like none other, control over the wizards and sorceresses, and demonizing the freedom-loving wizards and "New World"ers, he's well on his way to actually ruling the world. He even has popular support, despite the terrible economic system that the Brotherhood runs.
Joseph Ander in particular, but the Anders in general, did this as a race, using guilt and political correctness to crush those who genuinely were trying to uplift them.
Jake Featherston, the Adolf Hitler analogue in Timeline-191. Elected leader of the CSA, he cripples Congress, emasculates the courts, tries to destroy the Confederacy's black population in a Final Solution, and invades the United States, planning to ruin them as a power forever more. In the end, he destroys only his own nation.
From Doctor Who, British Prime Minister Harold Saxon, AKA The Master, an insane Time Lord, notable for having strong public support (using the ArchAngel network to subtly hypnotise them), being honest and open with his Cabinet giggling at them, throwing the paperwork in the air and then having them all poisoned, taking a strong stand in diplomatic relations with the US President (having him murdered on national television) and bringing about dramatic electoral reforms (taking over the world). Vote Saxon!
Call of Cthulhu campaign The Fungi from Yuggoth. The Brotherhood of the Beast plans to cause worldwide disaster so its leader can step in, save the world and be made President of the U.S. (and eventually ruler of the world).
The Wizard of Oz as presented in the musical Wicked, though he is a more sympathetic example than most, being manipulated by Madam Morrible into thinking what he is doing is helping the people acheive their true potential.
Wintergreen is basking in this status at the second act of Let 'Em Eat Cake.
Darth Revan has more then a few elements of this in Knights of the Old Republic, especially considering how loyal his followers tend to be to him and/or his ideals even in the sequel, when he's been gone for at least five years.
Well, his followers who aren't Malak, at any rate. Of course, Malak proceeded to (try to) set up his own cult of personality, although he was somewhat overshadowed by Revan even then. And the big honkin' tombs of the dead Sith Lords of Korriban suggests this is something of a tradition.
Zachary Comstock styled the secession of Columbia as this, saying that the United States condemning their destruction of Peking was a sign that it had fallen irredeemably into apostasy. Comstock's actual control of the city was something he had secured since its founding (although it's implied he had rivals who were violently removed early on, probably on similar grounds). Comstock justifies all of this by invoking divine sanction indicated by his visions of the future.
In The Gamers Alliance, Dylas and Pronin pretend to be saviours of their people but are actually power-hungry tyrants who use people for their own purposes and aren't afraid to break a few eggs to make an omelette.
The ancient Greeks called this form of government a Tyranny. In their political phraseology "Tyranny" meant not necessarily rule by The Caligula, but rule by an autocrat who rules based on force and popular sentiment rather then by Royal Blood (who could of course be The Caligula but was often just a Magnificent Bastard). Such rulers were common in Ancient Greece and some were well liked and reasonably good at their job. In any case the Ancients were quite familiar with Glorious Leaders making this Older Than They Think.
Because of translation errors, political titles, military ranks, and propaganda messages; there are multiple variations. The common variations include the words: Leader, Ruler, Marshal, and General. An internet search is recommended for more information since listing all of their titles is not realistic.
In a similar case is Idi Amin whose full title is His Excellency President for Life, Field Marshal Al Hadji Doctor Idi Amin, Lord of All the Beasts of the Earth and Fishes of the Sea, and Conqueror of the British Empire in Africa in General and Uganda in Particular..
Augusto Pinochet set himself up as this following his Military Coup in Chile, portraying himself as the saviour of Chile, while destroying the nation's democratic institutions, and killing 3000 of his people.