I'm surprised no-one pointed Lana Lang out, especially considering how much people complained about her character being this. 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) astounds me and becomes blatantly obvious that she was a Creator'sPet and Author Avatar. 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. In Game of Thrones, the badasses Jaime Lannister and Barristan Selmy both speak very highly of Ned's reputation as a fighter. When Ned and Jaime, Dayne's successor and seen as the premier swordsman of Westeros, duel, Ned matches Jaime 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, while the book states that Ned never matched Brandon's strength and abilities as Brandon was seen as among the better swordfighters in Westeros.
In the books, Shae is a shallow prostitute that does little more than sleeping with men and telling 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 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. 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.
This generally happens when female rangers and less active male ones in Super Sentai are adapted for Power Rangers. The necessity of adding unmorphed fights and Power Rangers-made fight scenes often results in traits that were implied in Sentai to become more apparent in Power Rangers.
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.
Likewise 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.
In the Doctor Who television series, Susan, the Doctor's granddaughter, was very much The Load and a Screaming Woman who spent a lot of time blubbering, despite being from the same time and place as the Doctor himself. The Expanded Universe's Susan is... well, not. Books, audio dramas, and the like don't hesitate to make her the sort of character you'd expect the Doctor's granddaughter to be like. How Badass is she? Remember how the old series Master was re-cast by appearing hideously disfigured upon his return? Well, recently, at least one corner of The Verse now has it that Susan used his Tissue Compression Eliminator on him, and it twisted him into the form we see him in in "The Deadly Assassin." The original actress voices her, too.
Also, the Peter Cushing Dalek movies have a much savvier and braver Susan... even though she's only ten years old, tops. Of course, she needn't actually be as young as she looks, but this was waaay before a lot of what it means to be a Time Lord had been decided; there's no sign she was intended to be Really 700 Years Old.
Elementary: 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.
And in Sherlock, Watson's military career is given much more emphasis, and it's repeatedly established that Watson accompanies Sherlock because he misses the danger and excitement of his army days. And a couple of times (like his original self), Watson is able to come up with some very well-reasoned deductions, even if they end up being wrong.
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!)