According to retired Scottish gangster Paul Ferris in his book Villains, the IRA had this status among the British underworld during The Troubles; British criminals sometimes took on money-laundering jobs for the Provos because they paid well, but Heaven help you if you informed on them or, worse, lost their money. It didn't help that most British gangland murders are committed over territory or by gangs in the same city, meaning the murderer was normally still within reach of the law and revenge from other gangs, whilst many IRA operatives could be back in Ireland before the bodies of their victims were even discovered.
Vlad the Impaler (otherwise known as Vlad Dracula) achieved this reputation with the Ottoman Turks. According to records of the day, he once stopped a Turkish army that greatly outnumbered his by ambushing its vanguard (away from the rest of the force) and mounting them all on spikes—not their heads, the entire person, usually still alive and screaming. The rest of the Turkish army was so appalled at the sight that it decided it didn't want to fight anymore. The man was so dreaded that upon Vlad's death, the Ottomans had his head hung from the walls of Constantinople to help convince people he was gone for good. Not surprisingly, Christian Wallachians were fond of him, not just for his martial successes but for his various social and economic reforms.
Referenced by the Heralds in Assassin's Creed: Revelations: "To all visitors seeking the head of Voivode Dracula: Yes, we have it. Yes, he's dead. No, you cannot see it. No, he will not come invade you again. It has been over thirty years, now please stop asking!"
There's a (probably apocryphal) story that a cart laden with treasure and gold was left overnight in the middle of a street in Vlad's territory, and was left completely untouched, so much did his subjects fear him.
Genghis Khan used this as his modus operandi. If you didn't submit the moment the Mongols demanded it, you were butchered. Simple as that. Genghis's subordinates were even worse than him in this regard; Genghis at least practiced a degree of brutal pragmatism in his campaigns in China. In the regions conquered by his generals, entire countries were left utterly devastated. On his death bed he told everyone to make sure the enemies in the next battle didn't know about his demise, so he could scare the crap out of people even when he was dead.
Pirates of the Atlantic in the 17th and 18th centuries. If you hove to and handed over the supplies and sailors they wanted (they ruthlessly took carpenters, coopers, and smiths especially) then they'd let you sail off. If you tried to run away or dumped valuables overboard... Heaven have mercy, because the pirates wouldn't.
Josef Stalin made a science of this trope. After he took control of the Communist Party, the show trials he arranged to execute his political opponents filled his cronies with such dread that they were terrified of invoking the wrath of the Vozhd ("Führer" in German or "boss" in English) and would never dare try to depose him. Rumors abound that Stalin eventually died from being poisoned, which is pretty much the only way anyone could have stood against him. There is also some evidence that his servants heard him dying but didn't summon any doctors for fear of what would happen to them if they were mistaken.
The nickname of Ivan the Terrible is actually this trope, "terrible" being a mistranslation. He was indeed feared by his subjects, primarily not because of his total death toll - his reign coincided with the golden age of Inquisition and the struggle between Catholics and Protestants in Europe, so he was a rather moderately brutal king by his century's standards. But he had an unpredictable personality, was prone to onslaughts of rage and liked the more alternative methods of capital punishment.
Saddam Hussein's closest advisors were so terrified of displeasing him that they told him he could beat the US armed forces. In 2003. He couldn't. He was so amazingly feared that during his trial, when he wandered in all disheveled and malnutritioned, the jury still reeled in horror. It's actually a testament to their courage they managed to find him guilty, so frightened were they of reprisals and reputation both. Even after being found guilty Saddam felt he still had full control of his country and DEMANDED he be presented with a firing squad like a true soldier, but as we know, he didn't quite get his final wish.
All South American and Latin American dictators are this. Fulgencio Bastista and Fidel Castro in Cuba, Augusto Pinochet In Chile, Jorge Videla in Argentina, Anastasio Somoza in Nicaragua and Leonidas Trujillo in the Dominican Republic.
Porfirio Diaz in Mexico played with this trope: While he was (and still is) hated in his time due of his iron-hand policies, he hardly was the most feared dictator Mexico had, only the most notorious one since he ruled for about 35 years. On the other hand, Victoriano Huerta (who succeded Diaz after executing Francisco I. Madero) was (and still is) the most hated dictator Mexico ever had, despise he only ruled for only one year, but the atrocities he did during his rule managed to outshine anything that Diaz did during his three-decade rule, to the grade there's an award in Mexico named the Belisario Domínguez Medal of Honor after the aforementioned man who opposed him, and Huerta's men killed him, not before cutting his tongue out from his corpse.
Basically every notable warrior (and a couple government officials too) got at least one mention of them being regarded as this by one of the other sides in the Three Kingdoms era of Chinese history, but Zhang Liao got to truly live up to this trope as he was able to rout a force of 100,000 with only 800 men, and was said to be so feared crying children would grow silent in his wake.
Its hard to imagine the Mike Tyson we know now-a-days to be the dreaded, but in his prime he was considered unbeatable and he truly terrified his opponents. It also helped that he played up his reputation by walking into the ring without music while unrelentingly staring down his opponent, psychologically unnerving them. Oh yeah, he hitbloody hard too◊.
Many successful military commanders have been this to their opponents. Napoleon terrified his enemies, as did Lord Horatio Nelson, to give two examples from the Napoleonic Wars.
Napoleon and Hannibal (from the Second Punic War) stand out as two of the only military commanders in history whose enemies have paid them the ultimate compliment of redesigning entire strategies specifically to avoid facing them personally in battle.
The Wehrmacht was this in the early stages of World War II. Indeed, after Fall Taifun bogged down in sight of Moscow, Chief of the German General Staff General Franz "a strong military leader with great powers of motivation is the most important factor for sucess" Halder invoked this trope: "The myth of our invincibility is shattered", he wrote. The man's mile-wide optimistic streak had helped him ignore the way the Wehrmacht had actually taken her first serious losses on the first day of the war with the USSR (in Bessarabia) and had suffered its first true setback in just the third week (at Smolensk). The British press actually reported the battle of Smolensk as a Soviet victory (which is true enough strategically, though it was a tactical-operational defeat), something that annoyed Joseph Goebbels to no end.
The Japanese Army would also count, across Asia people would run and hide when Japanese troops were approaching. While they were afraid of being killed, they were mostly afraid of having everything they owned stolen and being sexually assaulted. Then again, they were also afraid of being conscripted into a work gang and doing heavy labour until they died from malnutrition and/or disease (if male, though usually aged 10-50) or being conscripted into a brothel and serving as a sex-slave until they died from malnutrition and/or (sexual) disease (if female).
Edward Teach aka "Blackbeard", the most infamous pirate in the world. Anyone who saw his ship, the Queen Anne's Revenge, would surrender immediately rather than put up a fight with him. He intentionally cultivated this sort of fear by, among other things, tying burning scraps of slowmatch (cord impregnated with gunpowder) into his beard to give the impression that he was on fire in battle.
The Royal Navy was this to the Italian Navy in World War II: while the Italian high officers thought they could win and control the Mediterranean, the sailors and the officers who actually sailed against the Brits (plus a few of the members of the high command) openly admitted they were doomed and their success would be measured by the length of their resistance and the losses they'd inflict before the ultimate defeat. Interestingly, the special operation branch of the Italian Navy had the same reputation among the Royal Navy, especially after that time they sank two battleship in Alexandria's harbor, one of which had the commanding admiral on board (the battleships were recovered and repaired, but remained disabled for months and the Royal Navy didn't dare to lower its guard for the rest of the war).
The Italian Navy (Regia Marina) was built with French Navy as the assumed enemy and to counter the French threat. Their cruisers and battleships were optimized to fight their French opponents. The Italian admirals never even thought having to face the Royal Navy. When they did, they were somewhat demoralized.
And it was that also to the Kriegsmarine. Grand Admiral Erich Raeder openly admitted to Hitler that his forces were so underpowered that all he could do was to fight bravely before the ultimate defeat. After the Operation Weserübung, which cost the Kriegsmarine two cruisers, one battlecruiser seriously damaged and dozens of destroyers, the Kriegsmarine was especially ordered to avoid the White Ensign and concentrate on the Red - the British merchantmen.
The Gurkhas. The Pashtun of eastern Afghanistan and Pakistan believe that the Gurkhas are immortal demons, who eat the bodies of the men they kill. Such is their reputation, it's said that during The Falklands War, a British captain casually radioed over to an attacking Argentinian vessel, informing them they had a company of Gurkhas onboard. Cue the Argentinian vessel immediately retreating.
The regular British military has a somewhat similar reputation for their bayonet charges. In the same war, just hearing a British officer shout "FIX BAYONETS!" would sometimes result in the enemy disengaging or even surrendering immediately.
Swiss mercenaries were considered the best soldiers in the world for several hundred years. To make sure everyone on the battlefield knew exactly who they were, they took to wearing outrageously colorful uniforms. The uniforms of the Vatican's Swiss Guard is a relic of this custom.
They were so feared that a treaty ending a war between several major powers specifically stated that no one was allowed to hire Swiss mercenaries. Ever.
Simo Häyhä, the legendary Finnish sniper who earned the most recorded sniper kills (505) in any major war, repeatedly wiped out mortar units and enemy snipers sent specifically to eliminate him and most impressively of all, only had iron sights to aim with. This eventually earned him the nickname of "The White Death".
Whilst being shot in the face, he simultaneously managed to take out the sniper that shot him, before lapsing into a coma. He awoke on the same day the Russians called a ceasefire, leading some to joke that the Red Army did so because they were too afraid of facing him again.
So feared of him were the Russians, they basically said "JUST NUKE THE BASTARD!" So they dropped an artillery strike on where he was thought to be. It didn't kill him.
Theodore Roosevelt. It was said that he died in his sleep because Death was too afraid to take him awake.
Honey badgers. They're famous for being avoided by every predator in Africa, and have been known to chase away elephants and eat (young) jackals and crocodiles.
Wolverines too. They've been known to chase away bears and cougars from their kills.
Golden eagles have been spotted chasing grizzly bears and scaring badgers not dissimilar to honey badgers away from a meal.
Notorious gangster Al Capone was terrifying both to the police and to rival gangs.
Diseases can be pretty terrifying in this way too, such as cancer or AIDS.
In the 1980s, AIDS was a mysterious disease no one knew about, except that it was fatal. Over time as more effective treatments and preventatives came out, it lost much of its dreaded title, though since there's no cure, it's still pretty dreaded.
Cancer comes along in so many different forms, each one more or less deadly than the others. While some cancers like squamous-cell carcinoma aren't very deadly, others like pancreatic cancer and lung cancer have much higher death rates and are considered much more threatening and scary.
AIDS and cancer are so dreaded that thinking you had it but being tested negative are known as AIDS scares or cancer scares.
In a humorous American Football example, Bernard Pollard is this to New England Patriot fans. He's caused no less than 4 injuries to Patriot players over the past few seasons, all of which completely altered the Patriots' seasons for the worse.
Fans will have their heart skip a beat if a star player on their team gets injured and they hear that the player has scheduled an appointment to see Dr. James Andrews. Dr. Andrews is obviously not a bad guy - he is very highly regarded and is considered one of the best specialists in knee, elbow, and shoulder surgery (three things which get hurt a lot in sports) - but if the player's going to see Dr. Andrews, it means the injury is bad (season-ending surgery is not infrequent).
In Cricket, the West Indies team of the 1980s, both due to the fact that they enjoyed one of the longest periods of dominance in international sport, and the physical intimidation from their fast bowlers.
In Ice Hockey it's the Canadians. Their Olympic team has more gold medals and total medal wins than any other hockey team in the world. The junior team is even scarier, winning fifteen of the thirty-six tournaments that have already passed and scoring 28 medals total. While the NHL results tend to be more mixed, the league is absolutely full of Canadian players, and it's worth noting that the team with by far the most Stanley Cup wins is still the Montreal Canadiens. Canadian players are also responsible for some of the most violent events in sports history, including the "Punch-up in Piestany," in which the Canadian juniors had a bench-clearing brawl against the Soviets that went on for twenty minutes before the officials blacked out the stadium. Their fans are also notorious for rioting, as any residents of Vancouver in 2011 will tell you. Essentially, Canadians try very hard to hold up their reputation of politeness... until you get them on the ice, and then all bets are off.
Worth noting that the USSR/Russian team is this to the Canadians, as they're one of the only teams that have records to match Canada's.
The American and Canadian women's national teams are this to everyone else. Any tournament these two teams are in (Olympics, world championships, whatever) tends to have the following result: Canada and the US will play for gold, everyone else is really just competing for third place.
When it comes to The Beautiful Game, Brazil gets to have this reputation. Many fans from other countries find themselves dreading the possibility their team will end up going against them in a World Cup, which will usually mean any winning streak will end right then and there. Other teams do get temporary Dreaded status, but they always get to qualify for it.
While American privateers during The American Revolution and The War of 1812 exacted a heavy toll on British merchantmen in general, the American heavy frigate USS Constitution quickly became this in the latter conflict, and much of her subsequent career. In fact, the Royal Navy in the Atlantic was under standing orders to never engage Constitution unless they could bring the entire fleet to action against her.
This was mainly due to the bulk of the Royal Navy, including her Ships of the Line, being busy blockading Europe and standing ready to face the French navy. The USS Constitution and her sister ships were so-called "Heavy Frigates", being very solidly built and rated at 48 guns. The Royal Navy's frigates were typically much lighter, carrying something like 28 lighter guns. This was mainly because unlike the US Navy, the Royal Navy (and most of her expected opponents) could afford to field a fleet of Ships of the Line, and thus had no doctrinal use for a Heavy Frigate (or an equivalent to the Americans' fleet of gunboats, which proved entirely useless against RN frigates.)
Rozalia Zemylachka, one of the last of the "Old Bolsheviks" to escape being purged by Stalin. Why? Because he was terrified of her. She was known as an extremely competent and sadistic soldier, and moreover one who was relatively content with her station in the Soviet state. She was just too psychotic to bother: as Verbal notes in The Usual Suspects, "how can you shoot the devil the back? What if you miss?" There was a good chance any attempt on Zemylachka's life would result in the death of the entire arresting force, and an extremely pissed-off and perhaps mildly amused killing machine out for revenge.