The biggest is definitely Meyer Lansky. In his first appearance, he's on the receiving end of jokes about being a kid in his dad's suit. Within twenty years, he will be one of the most powerful men in America.
Richard Harrow starts out as a unemployed, disfigured Shell-Shocked Veteran whom Jimmy Darmondy meets in Chicago. He quickly becomes one of Atlantic City's deadliest hit men and in season 3 he pretty much singlehandly ends a Mob War when he pulls a One-Man Army and slaughters more than a dozen armed gangsters within the span of 15-20 minutes.
The show is one long study in this trope for Walter White. In season one he's a mild mannered science teacher living in a near shell shocked state over all the disappointments and missed opportunities in his life, and, unknown even to himself, is secretly enraged by it all. By the end of season four, he's toppled a major drug ring, murdered a LOT of people, and in season five, is the Big Bad of his own story.
Gus Fring. A flashback shows him as a mild-mannered fast food cook on the bottom rung of the drug trade who watches helplessly as the cartel murders his friend and partner. In the present, he's become the ruthlessly competent and dangerously savvy head of an international drug empire.
Liam was just a cheap and fun loving young man, just one of many in the world who would have lead an unremarkable life — until he met a beautiful vampire. Reborn as Angelus, he immediately distinguished himself from other vampires by his sheer cruelty and inhumanity. Even the Master, one of the oldest and most powerful vampires seen in the series, called him "the most savage creature I have ever known". Despite being not much stronger than the average vampire, Angelus always inspires fear and dread whenever he reasserts himself. During his stint as Big Bad he came closer to destroying humanity than anyone else in the series, even the First Evil itself.
Really, this applies to nearly all the Master's line: Darla, Drusilla, and Spike started out as, respectively, a High-Class Call Girl dying of syphilis, a chaste and timid young woman suffering from unwanted visions, and a Momma's Boy who write bloody awful poetry. Who would have expected the likes of them to become a crew of Hero Killers?
Willow went from a powerless, clueless Muggle to the most dangerous member of the Scoobies and probably the most powerful magic user on the planet over the course of six seasons, but didn't become a Nightmare until Tara was killed and she went on an Unstoppable Rage rampage that almost ended with the world ending. Jonathan, having known her almost as long as Buffy and Xander, could hardly believe she was the same person.
Warren Mears at first seemed to just be some pathetic geek living in his mom's basement, until he showed up at Buffy's place with a gun.
Arguably, the From Nobody To Nightmare happened in the episode Dead Things. Before this episode, Warren was presented more like Jonathan and Andrew, i.e. immature geeks trying to act like comic book supervillains, though he had been the only one willing to have a demon kill Buffy in "Flooded" and tried to dissolve her in "Gone" instead of re-visibling her. However, in Dead Things, Warren mind controls his ex-girlfriend, then proceeds to try and have sex with her, and then crosses the Moral Event Horizon by accidentally killing her when she wakes up, then manipulates Jonathan and Andrew into framing Buffy for murder, using magic so even Buffy believes she's the killer. Then he just gets worse from there...
The Mayor. He was originally a mortal human, stumbled across the Hellmouth while prospecting for gold, and made a deal with the demons (which included the founding of Sunnydale on the Hellmouth and his gaining immortality) mainly in order to avoid being killed.
The comic story "Haunted" reveals Adam was just a random, faceless Initiative grunt killed by the Mayor.
Discussed at the end of the episode "Damage" in the final season of Angel. The episode concerns a woman who when she was just a young child, her parents were murdered by a serial killer and she was abducted and tortured by him, literally driven insane. In the present she inherits Slayer abilities and Super Strength, and the result is a rampage with multiple deaths. At the end of episode she's tranquilized and taken by the other Slayers, but Spike is pessimistic about their chances of being able to help her.
Spike: She's too far gone for to help. She's... one of us now. She's a monster. Angel: She's an innocent victim. Spike: So were we, once upon a time.
The Senior Partners, the Big Bads of Angel's spin-off show. Back during the Primordium Age when the Old Ones ruled the Earth, they were, according to Illyria, weaklings who were barely considered stronger than a vampire. In the here and now, they're all-powerful extradimensional beings who pretty much control our world and more from behind the scenes.
In the IDW comic series After the Fall, the various Demon Lords who took over L.A. when the Senior Partners sent the city to Hell were, for the most part, originally just low-level demons who took advantage of the chaos to build their power bases.
The Day of the Triffids: Torrence from 2009's version sees the collapse of society as an opportunity to get himself a nice suit and an army of mercenaries and try to take over the country.
Doctor Who: In the serial Planet of Spiders, the main (human) villain, Lupton, was a former salesman and manager for 25 years who was embittered when his company fired him. So he volunteered to do the bidding of giant spiders, who gave him great powers.
The Master. Before he looked into the Untempered Schism and had the drum beat implanted into his brain, he would just have been a harmless Time Lord child.
The Snowmen reveals that classic Who monster the GreatIntelligence started out as a parasitic lifeform in the form of sentient snow, feeding on the negative emotions of a single misanthropic man for most of his life, until it eventually developed a mind of its own and became magnitudes more deadly.
The Doctor, who is a demonstration of what happens when a member of the most powerful race in the Universe, decides to ignore their non-interference policy, steal a time machine and interfere!
Pretty much all Time Lords have the potential to be this. Even the first one Omega, who, according to Big Finish, started out as a student with bad test results and becomes someone who nearly destroys the Time Lords.
From Big Finish Doctor Who Sebastian Grayle. He was originally a Roman Soldier who didn't have enough money to marry his love. He is given immortality by the Nimons, and after living for centuries, outliving everybody he marries, becomes a bitter twisted figure who helps the Nimon invade Earth. He becomes so terrible that when he goes back in time his past self kills him.
Farscape: Namtar was a lab animal given a serum that boosted his intelligence. By the time the crew meets him he's an Evilutionary Biologist who terrifies everyone around him.
Heroes: Sylar/Gabriel Gray goes from a nebbish clockmaker to Social DarwinistSerial Killer supervillain in a pretty short period of time. Even among other super-powered people, he's one of the most powerful and feared.
House of Cards: Both the original and the U.S. remakerevolves around this trope. Francis Urquhart/Underwood was perfectly happy helping the Prime Minster/President's agenda, so long as he was promoted to the main cabinet/Secretary of State. Then the Prime Minister/President broke their deal, deciding Francis was better use to him as chief whip, a job Francis has held for twenty years. Cue the entire plot of the show, which is essentially Francis casually destroying everything his former "friends" have worked so hard for. All the while carrying a proud smile on his face. Being based on Macbeth, the show gives us the interesting twist of having said nobody to nightmare explain his plots, schemes, and motivations to the viewer, accompanied by a frequent Aside Glance.
Similarly, Stanley H. Tweedle, a technician fourth-class (lowest level) who had been nothing but a complete failure until fate intervened and he became the captain of the Lexx, which had the greatest destructive force in both universes.
Not to mention his first introduction. He was very convincing as the innocent Henry Gale, making it virtually impossible for anyone to Spot the Imposter. Then he began to show his manipulative nature that we're all familiar with, starting with stringing Locke against Jack even further which had horrible results.
Hell, the Smoke Monster was just a guy who wanted to escape from his jerkwad mother and sniveling brother. But then he gets pushed too far murders his mother, gets murdered by his brother, dumped in a magic spring, and becomes the mass-murdering Big Bad monster.
Once Upon a Time: Rumplestiltskin. Started out as a cowardly, crippled, wool-spinning peasant; then somebody made the mistake of threatening his son. Cue burning down the Duke's palace, killing an all-powerful evil sorcerer, and taking on said evil sorcerer's power, making ol' Rumple possibly the baddest dude in the fairy tale world.
Regina also would have been a nobody were it not for her ambitious mother. If Regina had had her way, she would have been the wife of a stable boy, her true love.
Regina's mother Cora was this. Twice. She rose from being a poor miller's daughter to a wealthy noblewoman and one of the most deadliest sorceresses in the world. Then again in Wonderland where she rose from being banished there with nothing but the clothes on her back to becoming the Queen of Hearts.
Power Rangers Wild Force: Viktor Adler / Master Org. Unlike most PR Big Bads before or after him, he started out as a completely ordinary man - an unassuming scientist with a crush on one of his two co-workers. Then he found the remains of the original Master Org and got much, much worse (without ever developing a split personality like Mercer and Mesogog).
Sliders: One episode features a world instantly cursed with twice its previous population because of the sliding technology. It's dominated by warlords who control the food supply. They meet one who mentions he used to be a shoe salesman.
In the pilot episode, Quinn is visited by another sliding Quinn, a cocky young man on his eighth slide, who helps him complete the formula for sliding. Many episodes later, Quinn encounters the same alternate version of himself, except his sliding experiences have turned him into a ruthless psychopath who has committed countless atrocities. He still has a tiny spark of humanity in him and wants "our" Quinn to kill him so that he can't hurt anyone else.
Smallville: Lionel Luthor was just a dirt poor kid from suicide slums with a set of drunken parents. Then after murdering his parents, he became one of the richest men in the world and the poster boy for Magnificent Bastards everywhere. His son Lex also goes from a privileged child in Metropolis to perhaps the most dangerous man in the world due to the accident that caused his hair loss and his dad's emotional abuse.
Stargate SG-1: The Replicators were built originally as just (semi-intelligent) toys who diverged so far from that original function that they became a Horde of Alien Locusts bordering on omnicidal mania, and eventually, an evil race. Oh, and yeah, not only were they a toy, but they were in fact a toy built by what was essentially another toy, a messed-up android built by a doddering old fool left alone on some backwater planet with nothing else to do.
Supernatural: Crowley used to be a 17th century tailor named Fergus MacCloud who, as Bobby put it, "sold his soul for a couple of extra inches below the belt". Over the centuries, he's managed to work his way up the demonic ranks to head of all deals, and later King of Hell, as well as making his mark as one of the Winchesters most dangerous and persistent enemies.
When we first meet Erica, she's a troubled, skittish epileptic ostracized by the entire school. Then Derek gives her the bite. Who's Laughing Now??
Torchwood: Miracle Day: Oswald Danes was just your average, run-of-the-mill sex offender on death row until everyone in the world lost the ability to die and everyone saw his lethal injection fail on live television. He was then recruited by an evil corporation as a spokesperson to help promote their corrupt agenda because vile though he is, Danes is a well-known figure and very charismatic. His Karma Houdini bites him in the ass however when the corporation reveal that he has outlived his usefulness and he goes back to being a nobody. On the run. From everyone.
True Blood: Bill Compton was just a random and lost confederate soldier dying of starvation as he tried to make his way back to Bon Temps to reunite with his family, who didn't even know if he was still alive. Cue one meeting with a lonely widow in a cabin deep in the woods and he was transformed into a vampire by the sadistic Lorena. He still remains somewhat of a nobdy for about a century after this until he is recruited by Nan Flannagan to be a spy for the American Vampire League and the Authority. A succession of seasons later, and he has become first the King of Louisiana to replace the fallen Sophie-Anne, a Chancellor of the Authority after Roman's demise, and now...a Humanoid Abomination that is the physical avatar of the vampire goddess Lilith.
The Wire: Young drug kingpin Marlo Stanfield just starts out the third season as a small-time player with a few corners, albeit ones that are considered prime territory for a dealer. His first appearance is about 10 seconds. Due to the arrest of his competition at the end of the season, he has taken over by the end Season 3. In the fourth season, the police see him as just another drug kingpin like the one before. By the end of Season 4, they start finding the bodies of his victims in row houses. A lot of bodies. Turns out Marlo is the most murderous, ruthless, and sociopathic man to ever run a drug empire in Baltimore.
The X-Files: Billy Miles is one of these. In the pilot episode, Billy is only a poor young man abducted by aliens. And this is the last we think we see of him. Seven years later, he is abducted again, is returned with an alien virus, and turns into an indestructible killing machine, bent on murdering Scully and her unborn child.