No other place in the UK Wizarding World is more feared or avoided than Azkaban Prison. It's loosely inspired by the real-world Alcatraz Island Prison but worse since Azkaban's guards are pretty much like wolves to take a bite out of their prisoners every now and then. Moreover, the design of the place is just gloomy and a Muggle prison might even be preferable.
Even so, Azkaban has housed some of the most powerful and dangerous wizards and witches to exist in the Harry Potter universe. Most of them are Death Eaters while some are just there because of anger issues or frame-ups. Needless to say, these are the individuals you don't want breaking out of Azkaban because of their notoriety.
RABASTAN LESTRANGE
Voldemort has no shortage of pure-blood wizarding families who pledged allegiance to him. The Lestrange family is no exception; they're like the Malfoys, except more twisted and more active in their support for the Dark Lord. One of them was Rabastan Lestrange, brother-in-law of Bellatrix Lestrange, who is an equally deranged pure-blood.
Anyway, Rabastan was famously responsible for taking part in the torture of the Auror Frank Longbottom and his wife Alice. What Rabastan did was so cruel that the couple went insane, leaving their son Neville, functionally an orphan. Rabastan's is presumed to be either dead or imprisoned after Voldemort was permanently defeated.
RODOLPHUS LESTRANGE
Rabastan wasn't alone in carrying out the hateful deed against the Longbottoms. His brother, Rodolphus Lestrange was also half to blame. Like Rabastan, Rodolphus was also sorted into Slytherin during their education at Hogwarts. That pretty much meant that his fate has always been to be a Death Eater.
Together with a similarly twisted group of friends, they formed their own junior Death Eater club at Hogwarts; this group included Bellatrix (his wife), Lucious Malfoy, and Severus Snape. Unlike Rabastan, however, Rodolphus managed to get escape Azkaban after Voldemort was finally defeated and went on to inform Delphini of her legacy and heritage, being Voldemort's daughter.
BELLATRIX LESTRANGE
Here we are, one of the most deranged members of the Black/Lestrange family tree. Bellatrix was born out of an evil union between the two pure-blood families who shared the same ideals as Voldemort. As such, Bellatrix is an unholy witch who has no qualms on killing his own blood whatsoever.
She displayed such amorality after killing his own cousin, Sirius Black. She also had a hand in capturing the Longbottoms which led to their horrid torture. There's no doubt that she's also a capable and dangerous witch and even managed to kill Dobby as well.
SIRIUS BLACK
Of all the prisoners in Azkaban, Sirius Black was the most undeserving to be there. He was merely framed and immediately imprisoned without trial for presumably murdering Peter Pettigrew. Still, even in imprisonment, Sirius proved to be a brilliant wizard as ever; he managed to escape the toughest prison in the Wizarding World without any assistance at all.
Sirius was able to do so by transforming into his Animagus form, a big black dog which is sometimes confused for the Grim. Such a transfiguration skill has to be learned and only a few wizards and witches are able to do so, which makes Sirius one-of-a-kind.
AUGUSTUS ROOKWOOD
Voldemort's spies can sometimes prove more dangerous and more powerful than his wizard and witch soldiers. Augustus Rookwood is a prime example of why spies are the most dangerous unit of an army. Rookwood initially worked as an employee of the Ministry of Magic but soon became a double agent for Voldemort.
There, he spied on the Ministry which later proved to be useful when Voldemort attacked the Ministry during the Second Wizarding War. Apart from the masterful espionage, Rookwood is also a formidable duelist and often uses subtle and deceptive tactics. He was only imprisoned because of Igor Karkaroff's testimony.
ANTONIN DOLOHOV
Among all of Voldemort's Death Eaters, Antonin Dolohov was perhaps the most notorious. He has the most successful portfolio as Death Eaters go thanks to his defeat of some of the most prominent members of the Order of the Phoenix. Hence, he's one of the most powerful wizards in Voldemort's army.
Among the powerful good guys Antonin has defeated was Remus Lupin (whom he also killed) and Alastor "Mad-Eye" Moody. Antonin was also able to fight Sirius Black; the two were evenly matched. As additional proof of his prowess, Antonin is one of the few wizards able to cast strong spells without words - even after Hermione used a Silencing Charm on him. The only person who was able to defeat him was Professor Flitwick.
BARTEMIUS CROUCH JR.
Sirius might have been the first person to escape Azkaban without any help, but Bartemius Crouch Jr. was the first person to ever do it. The more amazing part was that he did it without alarming the whole Wizarding World. Turns out, his mother and father helped him. Afterward, Bartermius continued to serve Voldemort without hesitation.
When he did, he caused one of the most dangerous Tri-Wizard Tournaments in the Wizarding World history. Barty successfully mimicked Alastor Moody, made Harry win the tournament, and thus resurrected Voldemort-- all in a school year's work. He thus proved that he was one of Voldemort's most effective Death Eaters.
IGOR KARKAROFF
Igor Karkaroff's appearance in The Goblet of Fire as a Durmstrang Headmaster can be confusing for those who haven't read the books. Originally, Karkaroff is an ex-convict of Azkaban and his crime was membership of the Death Eaters and torture of Muggles.
Karkaroff was only released after he struck a deal with the Ministry: his freedom in exchange for all the other Death Eaters. Despite his dark past and proficiency in the Dark Arts, Karkaroff was very much qualified to be a Headmaster in Durmstrang because of its different philosophies. Still, it takes a powerful Dark Arts practitioner to become a leader in that place.
LUCIUS MALFOY
Power isn't just strength or the physical capacity to exert force or one's skill; it can also be status, wealth, or ideals. Lucius Malfoy, in that regard, is a powerful wizard from a pure-blood family and a loyal servant of Voldemort. He was tried for Azkaban a couple of times but still got away free because he was pardoned (most likely due to his influence and money).
In Voldemort's absence, Lucius also served as the acting commander of the Death Eaters which was apparent in The Order of the Phoenix. Even after Voldemort was defeated, Malfoy's power, wealth, and status remain unshaken.
PERCIVAL DUMBLEDORE
No, not our powerful and departed Albus Dumbledore but rather, his father, Percival Dumbledore (who still bears a striking resemblance to him). He wasn't necessarily a powerful wizard but being a father of the greatest wizard of all time is enough to put him in this list. Anyway, Percival actually got sent to Azkaban after he vengefully attacked three Muggles who assaulted his Muggle wife, Kendra. The assault on Kendra also left her in a delicate condition where she was sent to St. Mungo's.
Apparently, that was enough to trigger life imprisonment for Percival (but Igor Karkaroff got pardoned despite having a worse crime). Sadly, Percival died while in Azkaban and his legacy was tarnished since people assumed that his beating up three Muggles was fueled by blood purity ideals even though his wife was a Muggle. Seeing Percival again and apologizing to him was one of Dumbledore's few wishes in life and his sole regret.