Christine "Chris" Robbins from Itazura Na Kiss has terrible taste in regards to men's looks Really terrible taste◊. She finds guys like Naoki ugly and guys like Kinnosuke sexy. It is implied that she got her tastes from her mother.
Naoki's own mother wonders why girls like him, due to his cold personality. Also, a gender swapped verison often occurs after people find out that Naoki married Kotoko due to her seeming to have no talents. That's likely because he has a "cold personality." (Looks aren't everything you know? Okay, maybe it is.) And yeah, Naoki is quite the Jerk Ass.
In the Gravitation anime, Suguru is surprised when he learns that the famous novelist Eiri Yuki, an emotionally reserved guy to say the least, is going out with the hyper, bubble-brained Shuichi and asks Hiro why Yuki would be interested in someone like Shuichi. Hiro replies, "That's what I'm trying to figure out."
In Full Metal Panic!, Leonard, the jealous Romantic False Lead, says something along these lines to Kaname about her love for Sousuke. He comments on how it's ridiculous that she likes Sousuke more than him, since Sousuke killed hundreds of people. Little does Leonard realize that he's fighting a losing battle when the object of desire is Sousuke.
Occasionally asked of Kousaka and Kasukabe in Genshiken. As it happens, Kousaka is actually a loving, caring guy... it's just it only comes up when his otaku switch is set to "off", and during ninety percent of his screen time it's "on".
Several characters in Nogizaka Haruka no Himitsu (especially students who attend the same high school Nogizaka Haruka and Ayase Yuuto do) wonder what the popular, talented and wealthy Nogizaka Haruka sees in average-looking Ayase Yuuto.
In Azumanga Daioh, some students wonder what their literature teacher's wife saw in him. To elaborate, said literature teacher is Mr. Kimura, who openly ogles girls half his age and once answered the question of why he went into teaching with a shout of "BECAUSE I LIKE HIGH SCHOOL GIRLS AND STUFF!" His wife appears to either not notice this or not care; given the amount of ditziness she displays in her appearances, it's more likely the former. It helps he's a decent guy when not being perverted (he donates large amounts of money to charity).
In Gundam 00, this is some people's reaction to the uber-serious, professional, and competent Kati Mannequin falling in love with an ineffectual goofball like Patrick Colasour. Some scenes in the series imply that she enjoys the fun he brings to her life: having him around helps her unwind and stop taking everything so seriously all the time.
Patrick: "Colonel! I've come to ask you on a date!"
Kati: "At a time like this!? The world is currently on the verge of a revolution. You don't have any thoughts on this?"
Patrick: "No! None at all!"
Kati: (Stunned Silence) *sigh* (smiles) "Wait, right here. I need to go change."
In Say I Love You, a few characters, particularly girls, wonder what Yamato Kurosawa, the most popular boy at their high school, sees in Mei Tachibana, a friendless outcast who keeps to herself. However, his interest in her is genuine, and keeps trying to get to know her more until she finally opens up to him. And despite that, several characters still try to sabotage the relationship, such as Megumi.
In the second Urusei Yatsura film, Beautiful Dreamer, Shinobu outright ask Lum this very question. Of course she's being a hypocrite, because she use to be Ataru's girlfriend herself.
During one episode of Panty & Stocking with Garterbelt, Stocking falls in love with a guy who's incredibly disgusting, foul, sexist and just all-around vile. Panty (and every single onlooker) wonders what Stocking sees in him. Even worst, the guy is quite obviously a ghost, raising even more questions. The question might have finally been answered during the Gainax Ending, when Stocking revealed herself to be a demon before she sliced Panty into 666 pieces.
Victor: If I live to be a hundred, I will never understand what you see in him.
Gert:None of us is going to live that long, Victor. That's the one thing Chase knows better than anyone...
In Wreck-It RalphthisFan-Art, Felix 2.0 is confused by the fact that a "high-def chick" like Calhoun would be married to anyone like his original.
Eddie Valiant's reaction to Jessica Rabbit being married to Roger in Who Framed Roger Rabbit. (Betty Boop's reaction, note, is "What a lucky girl".) In due course, Eddie does ask, and gets told why. "He makes me laugh!"
She also seems to imply there are other reasons...
Eddie: Better lover than a driver, huh?
Jessica: You better believe it, buster.
Note that from the Toons' perspective, it's the other way around: they're trying to figure out what Roger sees in Jessica.
The "Stepsisters' Lament" from Rodgers and Hammerstein's Cinderella:
Why would a fellow want a girl like her, A girl who's merely lovely? Why can't a fellow ever once prefer A girl who's merely me?
In Wolf Creek, Ben is travelling with two girls, hot, curvy blonde Kristy, and skinny brunette Liz. Guess who he has a crush on.
In Wedding Crashers, Claire is engaged to Sack Lodge, who cheats on her and inflicts multiple acts of savage brutality on the protagonists.
In Mean Girls, Kady asks this of Aaron about Regina. He asks the exact same question of her, except in a more friendship-oriented way.
In a review of Star Trek: The Motion Picture, it's said of Decker that it's clear what he sees in an alien character: "his reflection in her (bald) skull. What she sees in him is never made clear."
The Haunted Mansion when Jim learns from Ramsley the butler that Edward Gracey thinks Sara is the reincarnation of his love interests and wants to marry her, he protests that she is his wife. Ramsley calmly admits that's true, but adds he can't see what [Sara] ever saw in [Jim].
In My Best Friend is a Vampire, Ralph has no clue why Jeremy ignores Candy, who's a blonde cheerleader and obviously very attracted to him, in favor of Darla. Jeremy cheerily ignores Ralph's commentary on the subject, as Darla does with her own best friend, Gloria, who can't figure out why Darla has any interest at all in Jeremy.
Birgitte Silverbow in The Wheel of Time series elicits this from almost every female character she gets to know. Birgitte is a blonde warrior, and many men find her attractive, but she has a stated preference for ugly men. The man to whom she is fated to love in every one of her lives, Gaidal Cain, is nobody's idea of handsome—with the exception of Birgitte.
In Harry Potter and the Goblet of Fire Ron asks this about what Hermione sees in Krum. Harry immediately points out that he's a famous international Quidditch player, to which Ron responds "Yeah, but besides that!"
In Jack Campbell's Relentless, after a conference with Rione and some officers, the officers' reaction to Rione's acts is to comment on how it explains things. Duellos explains to Geary that they had wondered what he saw in her; now, they know.
The protagonists of Warrior Cats often wonder why the arrogant Berrynose attracts Poppyfrost and Honeyfern.
In P. G. Wodehouse's Jill The Reckless, Barker wonders this about Jill's engagement to Derek. Mrs. Barker urges his good looks.
Jane Austen's Mansfield Park: Fanny Price often wonders at what Edmund can possibly see in Mary Crawford. She admits that Mary is beautiful, spirited, and witty, but she's aware that he's blind to her faults and twists facts so that they would fit to his ideas. Of course, Fanny is the jealous variety since Edmund is her only friend and teenage crush.
The narrator of Jane Austen's Northanger Abbey observes this about Mrs Allen: "Mrs Allen was one of that numerous class of females, whose society can raise no other emotion than surprise at there being any men in the world who could like them well enough to marry them."
Live Action TV
In Smallville, Clark does a variant by telling Chloe he can't see what she sees in Davis. She denies being with him at all. Kind of justified given that he is Doomsday...
This happens in Popular when Josh the "cool" jock hooks up with the unpopular "fat girl" Carmen, and everyone is completely horrified, Harrison (for reasons best known to himself) writes a song about the absurdity of Josh finding Carmen attractive and performs it in front of everyone). It's basically an in-universe example though, as Carmen is blatantly a very pretty girl - albeit in a quirky way - and is only really "fat" by Hollywood standards. To the unbiased observer they don't seem an ill-matched couple at all (if anything, she's better-looking) but whether the makers of the show did this deliberately to demonstrate how pointless generic standards of "beauty" are, or whether they just couldn't bring themselves to cast a genuinely obese or unattractive girl in the role, is open for debate.
iCarly: In iEnrage Gibby, Carly, Sam and especially Freddie are dumbfounded that Gibby can get someone hot like Tasha as his girlfriend. They all agree in the end that "There's something wrong with that chick."
Friends: After discovering Monica and Chandler are dating, Phoebe and Rachel comment that "she could do better". Played with as Chandler, despite his neuroses, is actually a great boyfriend and he and Monica are very happy together. (Plus she has plenty of her ownissues so they're well-suited.) As Rachel and Phoebe have failed to establish a successful relationships themselves, its a justified case of You're Just Jealous than them having any resonable critcisms.
Howard (a perverted Casanova Wannabe) with Bernadette (a cute, bubbly, sweet girl) in Big Bang Theory. The funny part was that they met due to a promise between Leonard and Howard years prior if either got girlfriends they would set the other up on a blind date, Penny set them up and was dumbfounded that it worked out as well as it did.
Married... with Children plays this both ways. One could wonder (and in fact, Marcy has openly questioned her about this on multiple occasions) what Peg sees in her balding, homely, minimum-wage earning loser of a husband, when she's been hit on by more attractive and wealthier men. Al, on the other hand, could be asked why he continues to stick with Peg when he'd be fully justified in kicking her out for her ridiculous sense of entitlement and freeloading without contributing to the family. The question is never really answered, since whatever the headaches Al and Peg give each other, they're still too attached to break up their relationship even when they could profit materially by doing so.
That said, this question is averted entirely by Marcy Rhoades/D'Arcy and her husbands Steve and Jefferson. Steve and Marcy were clearly attracted to each other because they were both greedy, selfish and materialistic, and the marriage eventually broke down as Steve began losing these traits. As for Jefferson, his relationship with Marcy is pretty clear-Marcy gets to display him as a trophy husband, while Jefferson gets to sponge off her without having to get a job. The fact that they also apparently have a really steamy sex life doesn't hurt, either.
In That '70s Show, Eric doesn't understand how can his friend, Hyde be attracted to Jackie, whom Eric can't stand (even calling her "the devil"), because she's shallow, self-obsessed and annoying. On the flip side, many people (including Eric himself on occasion) don't understand what the heck Donna is doing with Eric.
Eric Donna? I just have to ask... why me? I mean there are so many other guys who are way better looking
Subverted when Hyde tries to explain his attraction to Jackie to Eric, making Eric realize it's not so much that Jackie isn't hot as much as her attitude is so annoying that it distracts him form her hotness.
Lee and Dawn in the British version of The Office. Lee is constantly shown to be miserly, misogynistic, joyless and a bully who, on various occasions, talks down to Dawn, outright offends her and belittles her ambitions. Done on purpose, since Lee is the Romantic False Lead who comes between Dawn and Tim, with whom she is clearly besotted. Given the show's aspiration towards low-key realism, it's odd that the show never explains why Dawn stays with Lee for as long as she does.
The writers freely admitted in this case that they had intended to make the Lee vs. Tim romantic rivalry more a battle of equals, each with their own merits, but fell into this trap partly because owing to the nature of the show Tim naturally had more opportunity to be presented as a more appropriate match for Dawn than Lee did. Although it didn't help that, when they were on together, Tim naturally ended up being more likable than Lee anyway.
The Christmas Special and Grand Finale somewhat answers this, with Lee being shown to have repeatedly squashed Dawn's hopes and dreams, to the point where she finally gave up having any dreams whatsoever and settled for the simple humdrum of day-to-day living. Tim's encouragement for her not to give up her dream of being an children's illustrator, leads her to finally stand up for herself and dump Lee's worthless hide.
In the U.S. series, this is Erin's reaction to Michael's pining for Holly Flax.
"I don't get it. I'm sorry, I just...I don't get it!...Is she an amazing cook or something?"
Considering Erin clearly came to see Michael as a father figure, it might have just been her being a jealousDaddy's Girl.
Also in the U.S. series, when Andy was engaged to Angela, Oscar flat out asks him what he sees in her.
The reality TV show Is She Really Going Out With Him? takes this question and runs with it, picking out a couple where the guy can, generally speaking, be referred to as a "tool" with no objection. In most episodes, the guy is shown as being uncaring (or having very messed up priorities regarding his relationships), insensitive, and an all-around jerk. Whether this is the reality of the situation, or the result of post-production editing is sometimes debatable, but when the boyfriend shows up to a formal dinner with his friends (who weren't invited) wearing very casual clothing (including muscle-shirts), it tends to be pretty clear why he and his girlfriend are on that show.
Played with in Keeping Up Appearances, where Hyacinth often wonders what her sister Daisy sees in Onslow (who, apart from being a lazy slob, is a fairly decent guy), despite the fact that Hyacinth herself is loud, brutish and unbearable to be around, to the point where her husband Richard dreads retirement because it would mean spending more time with her.
Comedian Graham Fellow's One-Hit Wonder song "Jilted John" is all about the 'moron' called Gordon who's stolen his girlfriend, although the song then subverts itself by saying "Just 'cos he better looking than me, just 'cos he's cool and trendy".
From Dragon Age: Origins, this is pretty much what Alistair says if you continually gain approval with Zevran.
Amusingly, he asks this to Leliana, who invokes All Girls Want Bad Boys and implies that she can also see the attraction.
Oghren will also ask Morrigan this in exact words, if the Warden is in a romance with her. Going by some other things he says to her, he's probably at least a little jealous. That and likely intends to steal your moves to pick up the ladies.
Morrigan herself will pose this question to a male Warden that romances Leliana instead of her. To a female Warden who romances Alistair, she will remark that he must be very good in bed, because she can't imagine any other reason why a woman would want him.
Leliana will pose this question to Alistair if a male Warden pursues a relationship with Morrigan.
Alistair poses this question to Wynne if a male Warden romances Morrigan. It's not so much out of jealousy, but more him likely wondering if he should find a straight-jacket for his fellow Warden, as they have quite clearly gone crazy.
Also, in Dragon Age II should a female Hawke romance Fenris instead of Anders, the latter will stop her and outright ask why, likening him to a dog.
If a male Hawke romances Merrill, rival Isabela will ask her what she could possibly see in Hawke, not knowing where to even begin listing his flaws.
Although never explicitly stated in-game, this must have crossed the minds of many characters in Monkey Island when Elaine, the rich, intelligent, gorgeous and independent governor, who turned down proposals of marriage from many eligible suitors, married a goofy-looking, dorky nobody like Guybrush Threepwood.
Etna asks Flonne this in Disgaea 3 when they start arguing over who gets to be Laharl's "wife" when they pretend to be Mao's parents.
Etna: Then tell me, what part of this made you want to marry him?
Mass Effect has shades of this with Female Shepard and Garrus Vakarian. Garrus is an alien species that looks more like dinosaurs than humans, but Female Shepard has the option to romance him in the second game. Garrus himself has little idea why, and in the Citadel DLC he even laments that people were looking at him with the same thought going through their own heads. Female Shepard doesn't give a damn.
Ace Attorney: Trials and Tribulations: Nobody has a clue what attracted Desiree DeLite (extremely attractive Biker Babe) to her husband Ron (a high-strung, nebbishly girly-boy) at first. Turns out it was a Rescue Romance.
If you follow Ittosai'sGood ending in Yo-Jin-Bo, this is the general reaction of the other guys. However, due to their tendencies toward jealousy, it comes off as "What does she see in him that I'm not better at?"
Many characters (justifiably) have this reaction to Lois' marriage to Peter in Family Guy. At one point, Brian asks her: "Have you ever stopped to think 'Wow I married that guy?'"
She doesn't answer him then, but she's thought about it.
Lois: My god, you're dumb. Thank god for that ass.
The canon answer is that she finds fat men attractive, and they share a sense of humor. Whether this is enough to make up for Peter's regular Jerkassitude is another matter.
Which seems to Retcon from an earlier episode when she couldn't form sentences when Peter became thin and muscular.
The Simpsons: Marge and Homer Simpson are (sadly) a milder version of this trope.
Some episodes answer the question.
In The Movie Marge actually can't come up with an answer to this question after his latest and most extreme bout of jerkassery and selfishness, and leaves him as a result. He does make up for all the dickish things he did, though, and they got back together.
Patty and Selma never approved of their relationship throughout the entire series. Upon meeting him when they were teenagers, they immediately hate him for no reason at all. They spend most of their time trying to separate them and pair Marge with someone else (usually Artie Ziff). Though, Selma is more tolerable to their relationship, because Homer helped her out and was jealous of their relationship. But Patty continues to hate Homer, even more so after she got out of the closet.
Sam says these exact words to Danny in one episode as he drools over Rich Bitch Paulina.
Some characters (and fans) notably Peggy and Mihn wonder why Luanne hooked up with Lucky in King of the Hill as he's a stupid, ugly, bucktoothed, middle aged, stereotypical hillbilly. You might ask what HE sees in HER. He's generally at least smarter and more mature than she is.
While other characters wonder this about Nancy and Dale as they rarely show their love for each other and Nancy cheated on Dale with John Redcorn for years. In fact, this trope applies for many couples in the series.
In the fourthseason of Kim Possible, Ron gets quite a bit of this when he starts dating Kim, even from the villains they're fighting.
Especially Dr. Dementor, who was more obnoxious about this than Bonnie Rockwaller, even.
Played for laughs in Flapjack. Peppermint Larry starts kissing Candy Wife, which causes this exchange:
K'nuckles: "There she goes again, givin' him kisses! What does she see in that guy?! Why doesn't she ever give ME kisses?!"