Lana Lang in the original DCU continuity wasn't even half as badass as she comes off in Smallville. Even at her best, she was the outspoken Daily Planet Editor who was a vocal supporter of an aged Batman. In Smallville Lana is apparently a kickass martial artist, skilled hacker, and master tactician whose skill could apparently rival that of renowned, albeit younger, Chess Master Lex Luthor, much to his chagrin and respect. Not to mention her highschool abilities, which despite being considerably lesser than what she became in later seasons, is still pretty much impossible to do for a high school student. Apparently she was a straight A student who was at least near the top of the class, regularly competed in high profile horseback tournaments, and to top it all off, somehow found enough time to run a sizable coffee shop as its manager and as one of its waitresses. How in the hell she had enough time, let alone the energy, to do all of this and juggle what was apparently a successful social life (she was a cheerleader for at least a season or two not to mention her general popularity with the other students) is a riddle for the ages. Again all these achievements listed above are solely from Smallville and aside from being popular and a cheerleader, had virtually no grains of truth in the DCU canon.
In A Song of Ice and Fire, Eddard Stark is a capable general, but is not particularly large or strong. Word of God states that Ned is a pretty average fighter and never as good as his bigger, stronger brother was. In the show, the badasses Jaime Lannister and Barristan Selmy both speak very highly of Ned's skills as a fighter. When Ned and Jaime duel, Ned matches the famous swordsman blow for blow and might be getting the better of the exchange before they're interrupted. Littlefinger also calls Ned "an even more impressive specimen" than his late brother Brandon.
In the books, Shae is a shallow prostitute that does little more than sleep with men and tell them what they want to hear. In the TV series she has way more attitude, seems to care genuinely for Tyrion and takes on a protective role over Sansa to the point of threatening another woman that was going to rat on her with a knife. She also carries the same knife while the city is under siege and says that she is ready to use it on any enemy soldier that tries to rape her.
In the books, Ygritte is just another spearwife wildling in terms of her combat abilities. In the show, she's a precision archer who's considered one of the deadliest members of the raiding party.
Ramsay Snow in the books normally hunts down defenseless women with a pack of dogs, and his most impressive martial feat was killing an elderly knight who thought they were allies until he cut off the man's arm. His father notes that he fights like he was chopping meat, with the strong implication that he'd be killed by any skilled opponent. In the show he's shown to relish battle and charges into a fight shirtless against armed and armored ironborn, emerging unharmed.
In the books, Brienne has a very awkward and insecure personality, while in the show she's far more confident and bossy. In the books, she's a skilled swordfighter, but tends to just barely survive her encounters. She's on the losing side of her fight with Loras before she tackles him, and only manages to defeat Jaime because of his emaciated condition. In the show, she defeats both Loras and Jaime rather handily and even defeats Sandor Clegane in both swordfighting and brawling.
In the novels, Stannis Baratheon may not be a slouch, but he prefers to lead as a general instead of at the front like his brother Robert. Not so in the show, where he leads the storm of King's Landing personally.
In a series that typically keeps most characters similar to the originals, Kat from Power Rangers S.P.D. is shown to be a better and more competent fighter than her counterpart in Tokusou Sentai Dekaranger. Unlike her counterpart, Kat does battle a group of mooks unmorphed, and generally is presented a lot more serious and determined. (This even continues into the episode where Swan/Kat gets a one-shot Ranger morph. Perhaps the only differences between the two versions of that episode: Kat fights the Mecha-Mooks unmorphed for quite some time; Swan morphs the moment they appear. Kat gets to do Judgment Time; Swan doesn't.) Also, Ben-G, who had had a beef with sentai Doggie for capturing him earlier, is now a general of the invaders who nearly wiped out Doggie's planet in the backstory, and gets a two-parter as Doggie tries to overcome his Heroic BSOD and avenge his world.
A minor version with the Fear Cats and Tyzonn in Power Rangers Operation Overdrive (Minor because it's confined to one battle.) While the Fear Cats school the Overdrive Rangers as badly as the Questers did the Boukengers, there's one difference: The Overdrive Rangers have some vehicles in their arsenal the Boukengers don't, and the Questers' power source interferes with the Boukengers' suits so badly they could barely stand, let alone fight, making the Sixth Ranger with the new power source the only one who could fight at all in his debut episode, while this plot point was left out of Power Rangers. This means where the Questers beat up on highly compromised Rangers who could barely stand, the Fear Cats were pounding the daylights out of Rangers who were fighting at 100% potential and breaking out things like flying bikes with laser cannons and the Mini-Mecha that once took out two monsters at once without breaking a sweat. It also means Tyzonn, the Sixth Ranger, must be very powerful, able to take them on singlehandedly and force them to retreat. Of course, Boukenger has the starting five get the upgraded power source and fighting the Questers became much more doable; this was not explained in Power Rangers but it's not unusual in either series - in any superhero series, really - for villains and heroes to be much more powerful when they debut, and the Fear Cats were still pretty tough, so nobody much said "wait a second, these guys were handing them their asses when they first showed up but now they're... handing them their asses a bit less!"
Agatha Cackle and her cronies in The Worst Witch were quite easily defeated by Mildred casting a spell to turn them into snails. In the TV series they manage to outwit her and reach the school, even succeeding in turning Miss Cackle into a frog. They return in the season 1 finale with another plan that comes quite close to succeeding.
Miss Cackle and Miss Hardbroom in the books were merely just the girls' teachers with little mention of their powers. In the TV series they are very powerful witches and demonstrate great power. Miss Cackle is able to freeze Agatha and her cronies effortlessly while Miss Hardbroom is able to stop a powerful magical blizzard that would have covered the entire world.
Elementary: While the Watson of this series is less physically capable than the Watson of the books, being a surgeon rather than an army doctor, her intellectual capabilities are enhanced. In the books, Holmes is the one who brings down Moriarty. In "Heroine", Watson is the one who figures out that Moriarty is in love with Sherlock and launches the plan to capture her.
Done once in a while in the Granada adaptations of Sherlock Holmes. For example, in "The Lady Frances Carfax", Watson chases down and shoots the villain at the climax (in the original the villain got away), and in The Solitary Cyclist, we get to see Holmes and Woodley's fistfight rather than just hearing Holmes mention it.
Irene Adler just wanted to be left alone with her new husband in the books. Here, she's a dominatrix who pawns Sherlock, knocks him out, makes Moriarty rage and brings the British government, Royal Family and the nation itself to its knees. Almost.
Irene gets this a lot in adaptations. A mastermind juuuust nearly Holmes' equal in genius, she pretty much always gets an extended role as his Catwoman and sort-of-almost love interest.
Mary Morstan, former CIA assassin who kicked ass while being pregnant at the time. Not a smart move to mess with her. Doesn't help she shot Sherlock.
In the comic, Lori would often fumble with her gun, and Carl saved her on more than one occasion. In the show, she is making headshots at night without panicking.
Maggie Greene went from an emotionally fragile girl from the comic to an emotionally strong and assertive in the show. Not only that, but the series also made her the most competent Action Girl of the group until Michonne joins in season 3. And if you take into account that Michonne is bad with guns, Maggie is still the group's ace female marksman. Not that Maggie is bad at melee either.
Good Eats often painted Louis Pasteur, father of bacteriology, as a heroic historical figure (as his discoveries led to improvements in food safety). One episode, "Milk Made", definitely fits the trope, as it features him taking down a Food Police helicopter with a flamethrower.note Looks like the Food Police got...pasteurized. (YEEAAAAAHHHHHHH!)