Yaegashi: I was just thinking what a strong woman you are, Koume. Koume: Huh? Yaegashi: But that strength is what makes you so attractive!
In Devilman Lady, Jason Bates says he would have liked Jun more if she was stronger than him.
In Kimagure Orange Road, Kyōsuke Kasuga definitely prefers Aloof Dark-Haired Girl ex-delinquent Madoka Ayukawa over clingy, sweet, ex-pseudo-delinquent Hikaru. However, he is the only one in his school attracted to her; pretty much all of the other guys are shit scared of her for her bad reputation. The rivals he worries about are quite a bit older (and mostly in his head)... And despite that, no one would dispute that Madoka is very beautiful.
In Urusei Yatsura the second test for a beauty contest is a strength test, and the third is a wrestling match.
Giroro fell for Natsumi from Sgt. Frog after she handed his ass to him in battle. She's now the only Earthling he doesn't want to destroy.
Sango is a demon hunter who wields a bone boomerang bigger than she is. While she doesn't receive much romantic attention throughout most of the series, both her canon love interests Miroku and Kuranosuke Takeda certainly appreciate that she can beat them all the way around the block and back. Takeda is the bigger example of the two; he fell into starry-eyed infatuation-at-first-sight while watching her beat the crap out of an enormous demon with the aforementioned boomerang.
Kagura is worth noting because the one girl to become Sesshomaru's Implied Love Interest was also the only one who dared to shout insults to his face.
In a manga omake, Ryuu-oh's father in RG Veda specifically tells his young son that he fell for Ryuu-oh's mother because she's "macho, strong, wild and cool". Amusingly, his wife says says she loves him for "being a good cook, sweet-tempered, clean and handsome". Ryuu-oh's conclusion? "YAY, I WANT A MACHO WIFE!"
One of the above page quotes comes from Cowboy Bebop: The Movie, wherein Spike is inspired to ask a cute Mars Special Forces officer on a date... while she's attempting to beat the crap out of him, and, considering that he's basically Bruce Lee, doing a damn fine job. The Lab Rat is also smitten with the same lady, and asks for a date in exchange for her help. She appears somewhat squicked by the thought.
Getter Robo: Armageddon—Kei takes a page from Ryoko and Mao and turns it up to eleven by defeating a Metal Beast (which had just finished utterly owning the rest of the army) while completely naked. The first things she's greeted with afterward are the simultaneous nosebleeds of all but two of her teammates.
Ophiuchus Shaina from Saint Seiya was liked by her student Cassios because she was the fiercest and most beautiful woman he knew. Seiya himself is enticed by her beauty and her strength, despite his stubborn refusal to fight her full force because she's a woman. Shaina doesn't approve!
In Code Geass, Worthy Opponent Gino is smitten with Fiery Redhead Kallen in large part because she's the best all-around female fighter (i.e. both as a mecha pilot and martial artist) in the series.
In Boku no Futatsu no Tsubasa Keigo suddenly decides to try and "catch" Mako after he sees her beat up a group of muggers trying to steal her mobile telephone.
Boa Hancock in One Piece is greatly admired by her (female) subjects because Amazon Lily follows the mandate of "strength equals beauty". And she has the worldwide reputation and the skills to back it up.
Ranma ˝: The reason Akane had to fight through a crowd of boys to get to school everyday was because it was full of these. She beat them up every day and they came back for more; Kuno takes them as a sign of affection. In the second Non-Serial Movie, Prince Toma falls for Akane because she slaps him in the face and scolds him for kidnapping and then humiliating her and the other girls.
Shakugan no Shana: Eita's introduction to Margery was her beating up thugs. Afterwards he has a goofy look on his face and asks for permission to call her 'elder sister'.
The Robotech based sequel Super Dimension Cavalry Southern Cross, has the known player, Charles de Etouard, chasing after the Ace Pilot Mary Angel - one of the three female protagonist of the show. Unlike the other women whose hearts he played with, Charles falls pretty hard for Angel.
Mikasa Ackerman and Annie Leonhart from Attack on Titan both have their fair share of admirers (or potential admirers), partially because they are two of the biggest Badasses around. Since the cast are soldiers, it's entirely justified that they would be attracted to physically and mentally strong women that can hold their own in battle. Eren in particular is immediately drawn to Annie because of her formidable skills, though the exact nature of their feelings for each other remain ambiguous.
The DCU and Justice League: Scott "Mister Miracle" Free and his wife, Action Girl Big Barda. Barda is a beautiful 7-foot-tall bruiser who towers over her husband, but that doesn't bother the super escape artist in the least. In fact, they are Happily Married, and he is so secure in his own skills and abilities that he gladly defers any heavy lifting or fighting to his wife, who is eager to smash the bad guys when appropriate.
Wonder Woman, herself a literal Amazon, is an Ur Example of this trope. In the Pre Crisis DCU, Steve Trevor, the beau of Wonder Woman, rarely showed concern about being overpowered. Post-Crisis, Wonder Woman generally doesn't get into romance either way—she just doesn't have time—but it's joked that small-time crooks will gladly get manhandled by her.
Rose Wilson/Ravager of the Teen Titans, who was the toughest member of the modern version of the team. Both her friends Kid Flash and Kid Devil harbored a crush on her, most likely because of her badass-itude.
Pictured above: Marvel Comics' Jennifer Walters. For the most part, the super-powered men of the Marvel universe can't get enough of her seven-foot, green alter ego. Her experiences with mundane men are rather well-documented, too, usually with the implication Jen in her She-Hulk forms is much more outgoing and confident.
The biggest example is Bon/Ryuji though, since he gets his own section in this regard. Though, aside from making him very attracted to Rin, it also makes him determined to Level Grind so that he will be worthy of her.
The Hunchback of Notre Dame: The reason why Phoebus went after Esmeralda. Clearly he was interested before, but when he saw her standing up to Frollo and kicking some ass... Yeah.
This is lampshaded when Esmeralda is nicely taking care of the guards Frollo sends after her. Phoebus ducks a metal helmet that she flings at him, Frisbee-style, looks totally love-struck, and comments "What a woman!"
Monsters vs. Aliens: Mad Scientist Dr Cockroach is noticeably smitten with Susan after she defeats the giant alien robot. Given his less-than-stellar looks size and species this has a certain element of squick.
Wreck-It Ralph: Felixfalls forSpace MarineSergeant Calhoun. She's rough, tough, and knows her way around a gun, in contrast to his niceness and innocence; their first meeting involves her knocking him to the ground and almost shooting him as he's admiring her. Later on, when they are both stuck in a dire situation in which she is forced to batter him repeatedly in order to escape, he smiles through each blow and compliments her strength as she's hitting him.
In Frozen, Kristoff was dismissive of Princess Anna at first. The first spark appears when she clobbers an attacking wolf with a lute.
Film - Live-Action
Lorna Cole in Lethal Weapon 3 has absolutely no problem matching Martin Riggs in the ass-kicking department, a quality that contributes greatly to their eventual romance.
Callahan from the Police Academy films. Her first combat demonstration ends with her asking for a volunteer and every man present jumping to his feet.
Ever After: Prince Henry is fascinated by the way "Nicole" climbs trees, swims alone, and is strong enough to hoist him over her shoulders.
Asha Greyjoy, from A Song of Ice and Fire, is lusted after half the male crew of her ship and even her own brother before he recognizes who she is. Note that she can raid and pillage with the best of them.
Cordelia Vorkosigan gained her husband in the midst of a war by impressing him with both her brain and her martial prowess. Droushnakovi is a female martial artist whose husband is not the least bit intimidated by her and instead finds her skill attractive. Elli Quinn and Elena Bothari, of the Dendarii Free Mercenaries also gain male attention not just for their looks but for their physical aptitude as well.
Miles himself has a thing for Amazons, given his relationship and infatuation with the aforementioned Quinn and Elena, respectively. Also, his occasional flings with Sergeant Taura are noted by a friend who calls it "mountain-climbing."
Black Sheba in The Pyrates is this trope poured into a leopardskin tracksuit.
Born a Barbados slave, she had clawed her way to power in the Coast fraternity by a piratical genius and ruthless ferocity that had made her the toast of women's liberationists all along the Main. Her fellow sea-wolves respected her, had astonishing fantasies about her, and went in terror of her, and she despised them all.
Many in Honor Harrington. For instance, Sergeant Major Iris Babcock, RMMC, is not particularly attractive. But her truly incredible badassitude note as in, she can throw the title character around the mat with absurd ease, and the title character is a black belt in the martial art they are sparring in leaves Horace Harkness absolutely speechless. The next time either one of them shows up in the narrative, they're married.
Ashlin, from Amanda Downum's The Bone Palace, is this, at least in the opinion of Savedra, Ashlin's husband's mistress, who finds her very attractive.
In the sequel, Legacy of the Dragokin: Benji has a crush on General Lydia and wants to become a hero partly so he can be a Battle Couple with her.note the other part of his reason is to emulate his mother.
Danny has his eyes on Sabrina, a squire one year his senior who can transform into a drake.
Doug was first taken by Briza's beauty but becomes even more smitten after seeing her skill with a sword.
Chris is Hot for Teacher and that teacher is the hand-to-hand combat instructor.
In Harry Potter, Harry and Ron fall for Ginny and Hermione respectively because of their strength and cleverness. In the case of the former couple, the film of Half-Blood Prince includes a scene where Ginny shuts up everyone trying out for the Quidditch team, by shouting them all down. Harry is noticeably impressed.
In Quidditch Through the Ages, the captain of a team defeated by the all-women's Holyhead Harpies knelt down on the pitch and proposed to their captain, who promptly cold-cocked him with her broom.
The Heroes of Olympus: Demigods tend to lean this direction, since they're frequently in mortal danger. Percy Jackson clearly feels this way toward his girlfriend Annabeth Chase for an easy example.
When the show introduces the new slayer Faith, Xander hangs on her every word. At which point Cordelia asks what's with him and slayers (knowing that he's had a crush on Buffy). Should she dress up like one and put a stake to his heart? He wished she wasn't kidding.
Riley Finn likes the fact that Buffy is strong, decisive and good in a fight, no doubt seeing them as a potential Battle Couple. Unfortunately this doesn't last when Riley is Brought Down to Normal; he can't take the strong supportive male role and Buffy refused to let him have that role or open up to him (as Xander puts it, she treated him like the rebound-guy for the duration of their relationship). Together they eat away at his self-confidence until he leaves. In the next season, it's revealed that Riley is in a more equal relationship with non-powered special forces Action Girl. He and his new wife are a picture perfect Battle Couple.
Spike is this for Drusilla, Slayers in general and Buffy in particular - it's not a stretch to say he's only interested in women who can (and do) kick his ass. Outright stated in the After the Fall comics.
Alias: Julian Sark is very attracted to action girls. He was romantically involved with badass females such as Allison Doren and Lauren Reed, plus he has a long-running crush on Sydney Bristow. The more these ladies showcase their skills, the more turned on he is.
Kara Thrace on the rebooted Battlestar Galactica seems to be surrounded by men who have absolutely no problem with the fact that she can, and probably will, outfly them, outshoot them, beat them up, and then drink them under the table. On the first date. Of course, the fact that those qualities make her a dynamite wingmate you want in battle would explain the pilots. Gaius Baltar, one of her one-night stands, is better known for his various liaisons with Cylon females — all of whom have been tall, intimidating, and capable of snapping him like a twig should they so choose. One was even played by Lucy Lawless.
Deputy Josefina "Jo" Lupo from Eureka certainly fits this trope. According to the show, she holds the all-time Army Ranger's marksmanship record. Consider this particular quote from the second episode of the third season.
On Stargate Atlantis, resident Big Guy Ronon Dex turns out to be one of these when he falls for one of the gate technicians after watching her take out some bad guys with her kickboxing skills.
The first season of Star Trek: The Next Generation features a visit to a planet where the familiar gender roles (before about the 1960s, in the west) are reversed—the women rule the world and are strong and aggressive, while the men are effete, perfume-wearing arm candy. Riker seems to like it, and happily makes himself the planet's ruler's Man of the Week, in a sort of manly way. Of course, this was before he (and TNG) grew the beard so it sucked.
It wasn't just the authors, either. Worf, in particular, seems to value asskicking in a lady, his relationship with Jadzia starts with the two of them having a little spar with some bladed weapons and him being impressed that she could actually fight on par with him.
From Glee: Though a bit on the wide side, Lauren is an intimidating teenager with a state championship in Greco Roman Wrestling. Puck likes her because of her attitude and has been hitting on her, but after she wiped the floor with Santana he practically asks her marriage.
Babylon 5's Susan Ivanova, The Lancer and Number Two. Marcus Cole is absolutely besotted with her, and becomes so after seeing her kick ass and take names.
Damien Scott in Strike Back shows distinct tendencies toward this; though he'll sleep with pretty much any woman anyway, he noticeably perks up and pays more attention when they start kicking ass and taking charge. Notable examples include the Tuareg leader and the Mossad agent in the Vengeance series.
Craig Ferguson, to his own surprise, found himself incredibly aroused by the idea that Gina Corano could kick his ass if she wanted to.
Psych: Lassiter looks EXTREMELY proud when he finds out his fiancee Marlowe used Muay Thai to beat up the thugs holding her and then jumped out of a window to escape. When he later thinks she climbed out of a very high window and shimmied along a very small window ledge to the fire escape, he proudly announces "Our children are going to be Seal Team Six members!" Then, when Lassiter rushes in to save her and she hits him, he says "Was that a spinning back fist? God, I love you" and gives her a Big Damn Kiss.
Alt-country singer/songwriter Kevin Welch has a great song, "Hill Country Girl," that exemplifies this trope. Lyrics snippet:
Atalanta from Greek mythology - a beautiful blonde who was also a skilled huntress and athlete. She had suitors lining up to try and beat her in a foot race. If they won, they would win her hand.
The Talislanta setting is home to the Danuvians, a near-human folk in which the women are Proud Warrior Race Gals, while the men are delicate and housebound. Polyandry is common, as many Danuvians keep both a beautiful Danuvian husband to father their children (no Half-Danuvian Hybrids here), and a husky non-Danuvian warrior husband, whose physical prowess and military background give them something in common to talk about. Thus, these warrior-women fulfill both sides of this trope simultaneously, where tastes in men are concerned.
One scenario in Osu! Tatakae! Ouendan 2 involves the Ouendan helping out Kaede, a former female pro-wrestler who marries the son of the owner of a ryokan (a traditional Japanese inn). He seems quite happy with the arrangement, and quite distraught when his mother threatens to throw Kaede out on her ear if she doesn't get up to snuff as a ryokan hostess.
Some of the canon pairings in Fire Emblem also fall into this trope of a guy falling for a Lady of War or Action Girl character and finding her charming because of her strength. These girls are:
The pirate Briggid, the thunder mage Tailto and the swordwoman Ayra from Genealogy of the Holy War as well as Ayra's daughter Larcei and her in-story Expy Radney;
Fir the myrmidon from Sword of Seals. In her supports with Noah it's explicitely mentioned that he fell for her when he met her in the arena;
Lady Lyndis of Caelin (Lyn), the swordwoman Karla who is actually Fir's mother and idol, for whom she took up the way of the sword, the Pegasus Knights Fiora and Farina, and the Dragon Lord Vaida from Blazing Sword;
Mass Effect has Gunnery Chief Ashley Williams, who is a possible romance option for a male Shepard. Some of the dialogue (if you use it) indicates that her fighting skills may be one of the reasons why Shepard finds her attractive. And female Shepard's own skills seems to be what Kaidan Alenko finds most attractive about her.
Part of the reason any of the male characters are attracted to Shepard is because of how much of a Badass she is. With Garrus the relationship developed from their friendship but also the incredible amount of respect he had for her.
During the time Foxhound was stationed at Shadow Moses to provide security, Otacon seemed to have become very fond of Sniper Wolf.
And there's Olga Gurlukovich in MGS2. Growing up as the daughter of a mercenary commander and becoming his second in command as an adult, and taking over as commander after his death certainly qualifies her as an action girl. And though we don't learn anything about her private life, at least one man must have felt drawn to her. Having a kid and all.
In Kingdom Hearts: Birth by Sleep, Zack asks Aqua on a date just minutes after she a) kicked his ass, and b) took on the God of the Dead and a copy of the Ice Titan single-handed. There's no way that's a coincidence.
Dragon Age II has a female Hawke, as well as Aveline, whom Donnic definitely thinks is attractive. Amusingly, it takes a long time for Donnic to get that Aveline's also interested because romance is the one place her backbone gives out.
Any of the female Warden's love interests count as this in the original, given how badass she can level up to be. Zevran doesn't mind "serving the whims of a deadly sex goddess", while a happily married Alistair tries to insist that "just because she killed an Archdemon doesn't mean she scares me!"
The main character of The Space Bar seems to be one. He has the major hots for a dancer in the eponymous bar who's a member of a species where the females are the dominant and strongest sex. Further, if he tries to kiss her she'll knock him to the ground with an uppercut and he'll whistle after picking himself up and be even more interested in possibly asking her for a date (though his PDA AI talks him out of it).
In Tomb Raider, Alex is revealed late in the game to have had a crush on Lara even before she became an Action Girl. However he's even more attracted to her after watching her take down the guards that were holding him and the rest of Endurance's crew prisoner precisely because of how bad ass she's become, making it this trope. Unfortunately, his fears of No Amazon Wants A Normal Guy leads to his death when he tries to impress Lara by returning to the wreck of Endurance alone to recover equipment needed to repair the crew's escape craft.
The King of Fighters: One of the reasons why Sie Kensou likes Athena is her Badass Adorable charm. In XIII, his win quote against her has him explicitely saying "You're so strong, I couldn't hold back!".
In Brutal Legend, the resistance leader's girlfriend shows up wounded and later refuses to tell the Player Character how she got hurt because he would stop her finishing the job. His response?
Eddie: No, that's Lars. I like watching you fight.
In Final Fantasy IX this is alluded to when Zidane is helping the princess escape. This is after he chased her around the castle, watched her jump off a tower and then swing to safety using a street decoration.
"Wow, you're really athletic. I think I'm falling for you"
Little Busters: In Kurugaya's route, Riki, who himself is a MoeNon-Action Guy, is mainly attracted to her because of how cool she is. The other male childhood friends find this inexplicable, as to them she's just terrifying. (Though to be fair, she'd far sooner hurt one of them than someone cute like Riki.)
A very downplayed example occurs in Tokimeki Memorial Girl's Side 2 with Hikami. Go touring with him on your second-year field trip and he'll attempt to lift a giant staff to fulfill the superstition that any man who can do so will have great success in life. The heroine suggests she should try, too, but Hikami tells her the superstition is Different for Girls: a woman who manages to lift the staff will be high-strung and dominate her husband. Hikami then muses to himself that things would certainly be interesting if the two of you were together, then quickly blushes and tells you that he didn't say anything and to forget it. This is especially surprising because Hikami is a bespectacledLovable Nerd who constantly enforces school rules, and he's normally attracted to your high Study stat instead.
Hiyoko Tousaka of Hatoful Boyfriend is the protagonist of an otome game. Her love interests are birds, and she's capable of throwing two out a window at once. She's also a Contemporary Cavewoman, seen as a barbarian, and has more emphasis on the hunter part of hunter-gatherer. Nobirdie is discomfited by this and several love interests have positive comments on her stature and strength, though most of the "romances" seem more like "forging close personal friendships".
In Girl Genius, Agatha and Gil are turned on by each other's Sparky inventions, which usually consist of large weapons they use in combat. At one point, Gil confides with Wooster that he'd always dreamed of meeting a girl who was a Spark of his caliber.
Paul Twister finds Aylwyn's strength and large stature very attractive, and the one time when he actually acts on his feelings is after seeing her fight a reanimated dragon skeleton.
Teen Titans: According to Robin, some of the things he likes the most about Starfire are "the way you shoot starbolts, ... that you're brave, and the strongest girl ever."
In Justice League, Wonder Woman may be one of the most powerful superheroes of all, and it apparently doesn't discourage most men lusting after her, including a DCAU version of Hugh Hefner. Even in a Time Travel story into the Wild West, the most significant reaction to her incredible power is from Bat Lash, a self-styled ladies man who notes admiringly, "That's a healthy gal!"
The Angry Beavers: The Girl Racoons parodied this in the season 2 episode "The Mighty Knothead".
While Dr. Holiday rarely throws down outside of her Mama Bear tendencies, there was a particularly epic moment she got where she saved Agent Six and Rex by rapid-firing at a huge monster, driving it back. Six's gobsmacked expression said it all.
This also seemed to be the point where Six started returning Holiday's UST for him.
Ron in Kim Possible. He's attracted to four girls over the course of the series: one is among the greatest warriors in Everlot, one is a ninja and the third is the show's heroine.
Motor Ed hits on Shego even more persistently after she lets him have it with a plasma blast.
His brother, Mako, also seems to be this. Initially, Mako's totally smitten with Asami but he falls for her before he learns how tough she really is. This trope holds truer in his second girlfriend, Korra.
From the original series, Sokka seems attracted to Suki in part because she's such an excellent fighter.
(watching Suki beat up a bunch of firebenders and capture the Warden)
Hakoda: "That's some girl!"
Sokka: (smitten) "Tell me about it..."
Texas might be this in Motorcity. He's shown a bit of a fondness for Kaia, as well as Julie after watching her fight robots in "Off the Rack." So far, he hasn't shown to chase any of the actual "Amazons" in the show.
In Adventure Time, Finn comments after his first meeting with Flame Princess— who demonstrates that she is both literally and figuratively Hot-Blooded— "I think I have a crush!" Later, he gets very... excited... when he sees her beat up the Ice King.