In a slight twist on the harem genre, none of the girls aside from Aoi in Ai Yori Aoshi ever really had a chance. To blow up any shipping attempts, the first few episodes makes it pretty clear that Kaoru can't/won't choose anyone other than Aoi.
In Asu no Yoichi!, Ayame is this towards Yoichi, although it's because of her sister Ibuki; the fact that she doesn't seem to spend much time with him; and when she does, she seems hostile. Then she wonders why he doesn't seem to romantically notice her.
Washizu is this towards Ibuki, who never really acknowledges his feelings, either because he can't say it to her directly, or when he tries, it gets misinterpreted.
In Clannad, pretty much any girl who's not named Nagisa in the anime. All of the main girls even show up at Tomoya's house in episode 18 with food after he got expelled taking the blame for a fight for Tomoyo. Tomoyo and Kyou even blame the awkward lunch date on him for not making it clear who he likes. But at the end of the episode, after a tennis game, Tomoya indirectly makes it clear who he wants to be with, crushing all of their hopes in one fell swoop.
For those of you who refuse to accept the Official Couple that the anime chose, luckily there are two episodes where Tomoyo and Kyou both get a shot with Tomoya, and how their lives would've played out had Nagisa not of been there. And there's always the Visual Novel too.
Mazinger Z: Boss had a painfully obvious crush on Sayaka. Of course, given that she's The Hero's Tsundere girlfriend and he's the Gonkish comic relief, he doesn't stand a chance (although some people would argue by the end of the original Manga, he actualy does have a chance, judging from how Sayaka acts in front of him, but by this time, either he realized he has no chance or he already become such a good friend with Koji, that he doesnt care about it anymore).
In Please Teacher!, Koishi is this in regards to Kei. Maybe if she acted in the first episode, but after that, her chances were blown.
The former trope namer, Daisuke/Davis Motomiya from Digimon Adventure 02 has a crush on Hikari/Kari (Girl) and sees her friendship with Takeru/T.K. (Boy) as a genuine romantic threat. He becomes very jealous, characterized in the English dub by Davis never getting T.K.'s name right (ex: T.J., T.A., T.L. instead of T.K.). The character dynamics vary between the English dub and the Japanese dub, but the lack of success of Daisuke's romantic pursuit is there for both. *
Leave it at that, shippers.
Krillin of Dragon Ball Z showed every sign of crushing hard on Bulma. She, of course, was deeply in love with Yamcha (until she wasn't) and Krillin himself was too easily cowed to even hint to her at his interest. Besides, he ends up married to another girl — Android #18.
In Dragon Crisis, Misaki, one of Ryuuji's classmates. She never really stood a chance, since he's snatched away by his older cousin within the first 5 minutes of episode 1, and is quickly taken away by Rose. Not that it stops her friend Mao from attempting to hook them up anyway.
Ai falls into this trope as well, although it's largely because she's introduced later in the series well after Ryuuji's already been with Rose for a while, and she doesn't attend the same school as they do. But despite that, she decides to show up on the fourth floor window of their school at the end of the series, which one of Ryuuji's friends wonders how she managed to get up there from the window.
To an extent, Korea from Axis Powers Hetalia borders on this with his two older brothers, constantly groping them and downright flirting with them. This is taken to a further extent with China in the strip parodying a dating sim game, in which he's given a 'yes' or 'no' answer to Korea's seemingly innocent question of "Do you like me?" No matter which option China chooses, it ends with either sex or rape.
Prussia can also be viewed as one, due to hints in canon that he's attracted to Hungary and/or Italy, both of whom are overtly paired up with other characters. He's even treated to the sight of Hungary and Austria being happy together on Christmas as he walks alone in the cold and tries to tell himself that he doesn't mind being alone at all. Ouch.
The Turkey/Japan/Greece triangle is marked as a Type 3 in the author's notes (Turkey and Greece both like Japan, Japan hasn't explicitly favored one of them over the other), but well... just take a look at the number of Turkey/Japan fics vs. Greece/Japan fics on Fanfiction.net. Needless to say, virtually all fans who believe that Turkey likes Japan also believe that he doesn't have a snowball's chance in hell against Greece, the one who not only actually gets enough page time with Japan to show just how well they get along but also has had Umbrella of Togetherness and Did They or Didn't They? scenes with him. Even fans who don't ship Greece/Japan and want Japan to be with someone livelier almost never consider Turkey to be a viable option. (He fares somewhat better in J-fen, though. Somewhat.)
FAKE has JJ, who cheerfully refuses to acknowledge that Dee 1) has a new man in his life, and 2) never even liked him in the first place. Also Berkely, who thinks of himself as a Romantic False Lead but really, really isn't. However, both of them give up on their crushes in the epilogue "Like, Like, Love". Berkley hooks up with Action Girl Diana and JJ surprise kisses his semi-partner Drake.
Gantz's main character Kei Kuruno kind of suffers from this, since his love interest Kichimoto has fallen for his best friend Kato. Reika also suffers from this, since her love interest Kei Kuruno has fallen for Tae.
Akitoki Hojo in Inu Yasha, and his modern-day descendant.
In Love Hina, while Mutsumi seemed likely to snag Keitaro due to Naru not being able to clarify her feelings for him, the other girls never really had much of a chance, particularly Shinobu and later Motoko. Su hints at liking Keitaro, but never really pursues it.
In Nogizaka Haruka No Himitsu, although she tries, Shiina never really had a chance to get with Yuuto, since the first episode makes it pretty clear he ends with Haruka.
Ryoga in Ranma ½ is chasing after Akane who doesn't even realize he's courting her.
Also, all of Ranma's suitors. One of them (Kodachi) even admits to Ranma that she knows he doesn't love her back, but that this will in no way stop her from continuing to pursue him anyway.
Almost all. Akane counts as the one exception, but even that's a little iffy at times, due to Ranma's Celibate Hero status.
Ren in To Love-Ru. The poor guy never had a shot. So much that his male half was essentially Put on a Bus and he remained as the very female Run for pretty much the rest of the series, who was naturally a haremette in the Unwanted Harem of his romantic rival. Ouch.
Harima from School Rumble is this with regard to Tenma and Karasuma, and Nara with regard to Tenma and Karasuma, Tenma with regard to Karasuma and some delicious curry...
Ichinensei ni Nacchattara: Touta (~7 years old boy) jumps on Iori (7 years old girl) and tries to kiss her every chance he gets. Being as how Iori is secretly a genderbent highschooler, this attention is very much unwanted.
Beauty Pop: Ochiai for Kiri, although he doesn't give up; possibly Billy for Kiri as well, but it's hard to say.
Juvia, in Fairy Tail, whose crush on Gray is so huge that it can get her to forfeit major battles and lose focus of absolutely anything she was doing before seeing him. Her rival in love isn't actually interested in Gray, though. There was just a misunderstanding. She does get to spend time with him, but until she joins Fairy Tail she's just a Stalker with a Crush.
Kyouko from Aoi Hana keeps pining for Yasuko, even though Yasuko won't even give her the time of day. Kyouko's plight gets worse when she finds out Yasuko is actually dating another girl, which means Yasuko is not rejecting her because of her gender, but for other reasons. The scene in which Kyouko begs Yasuko to give her a chance after all has to be one of the saddest in the series.
In Pumpkin Scissors we are given Schultz and Alice. Schultz likes Alice even enough to shamelessly pursue her even though she's engaged to Leonir Taylor. This is not out of selfishness really; Alice was, after all, put into an arranged marriage with Taylor. However, chances are even if she wasn't engaged, she would probably not consider Schultz because of her dedication to her job.
Randoll from Future GPX Cyber Formula is this for Asuka. He has a crush on her despite the fact that she's in love with Hayato. In fact, he and Hayato once competed for her love. He keeps on presenting Asuka with little gifts, even after Asuka's engagement to Hayato.
In a completely odd turn around, Hayate the Combat Butler has something of this between Hinagiku, Ayumu and Hayate. Hayate does notice Ayumu's affection for him (helped by the fact that she's the first of the unwanted harem to have confessed), even stating that they could have been dating, but realizing that Hinagiku is the one he's infatuated with, Nishizawa has taken to this trope herself, and is trying to get Hinagiku to admit her feelings to him. It doesn't help at all that Hinagiku is trying to play matchmaker between Ayumu and Hayate because I Want My Beloved to Be Happy.
Also, Miki for Hinagiku, Miki realizes the Incompatible Orientationness of her situation, to her regret. But that doesn't stop her teasing of Hinagiku one bit.
The Ouran High School Host Club manga gives us both Hikaru AND Kaoru as Hopeless Suitors for Haruhi's affections. It's mostly Hikaru since Kaoru decides to confess to Haruhi telling her he loves her, but that there is still someone more important to him (his brother). After this Kaoru tells Hikaru he's stepped back and will support him as he goes against his love rival, Tamaki. It was already a losing battle for Hikaru, but he gave it a try anyway.
Wandering Son plays several characters affections as this, both minor and major. The most apparent is Mako and every boy he's ever liked, and Saori with Nitori.
In the SHUFFLE! anime, although the series teases us as to who Rin ends up with, the biggest loser is probably Kaede, the girl he's living with.It gets worse when Rin does choose a girl to spend time with, and causes Kaede to go a little Yandere. Averted in the Visual Novel however, since you get to choose who Rin ends up with.
Nanami may have a chance for Sorata prior to Mashiro's appearance, but after that, she falls right into this trope.
Played with both Misaki and Jin towards each other. While they do like each other, especially Misaki towards Jin, due to his womanizing ways and the fact that he always seems to brush off her advances. Jin on the other hand, feels he's not worthy enough to be with her, due to her talents, such as in animation, and feels he would just weigh her down if he tried to have a serious relationship with her. This despite the obvious signs that Misaki really wants to be with him.
In Quantum And Woody, Eric Henderson (Quantum) has this with his longtime crush Amy Fishbein.
Wolverine is this for Jean Grey aka Marvel Girl in pretty much every media safe Ultimate X-Men (though this also didn't last long).
Bernie Kuntz, a hopeless-dorky overweight appliance salesman with a bad combover toward Stephanie Plum, the spunky, ridiculously-attractive heroine of One For The Money.
The three sons of the three lords in Brave who are competing for Merida's hand in marriage and are all undesirable in her eyes. At the end of the movie, the three sons reveal that they didn't want to marry just yet either.
Housemaid Rosanna Spearman is hopelessly in love with protagonist Franklin Blake in The Moonstone. Hopelessly because not only is he a 'gentleman' and so out of her class but he's in love with Rachel Verinder.
Lettice Protheroe for Lawrence Redding in Murder At The Vicarage. He is in love with her stepmother, however. He is also a murderer- and her stepmother, too- so his indifference is probably for the best.
Michael for Rosamund in the Knight and Rogue Series. He actually helps to reunite her with her love, figuring that if she tries a few days of Ruby's less glamourous life stlye she'll be disenchanted. He's wrong.
It’s genderflipped with Tabitha, who falls in love with Marcus and hopes he’ll propose, only to be disappointed by his lack of attention because he is pining for Hadassah despite thinking she’s dead.
Live Action TV
In Smallville, it is a poorly kept secret that Chloe wants Clark for the first part of the series, while Pete in turn secretly wants her.
In Grounded for Life, Brad pined after Lily and assumed that her emotions were divided between himself (whom she barely noticed and openly discouraged any kind of advance) and her boyfriend Dean (whom she was all too ready to get hot and heavy with). Eventually Brad decided to "back down" and openly referenced the concept that they were in a "love triangle" to Dean, whose only concern was "The two end points don't touch, do they?" Though it might have been subverted later on when Lily broke up with Dean and ended up dating Brad anyway. Who's hopeless now?
Steve Urkel in Family Matters is a special case in that he knows he's the Hopeless Suitor — he's just not willing to let that stop him, hence the Catch Phrase "I'm wearing you down, baby!" His only shot at Laura was the transformation chamber that turned him into Stephan Urquelle, the epitome of smooth and cool. Steve Urkel himself managed to win Laura over in the shows last season, after some 8 years of Laura insisting on Just Friends.
There are elements of this in Sheriff Carter's relationship with Allison Blake in Eureka, especially after she agrees to marry former husband Nathan Stark for a second time. Even to the point that when Stark sacrificed himself, Carter decided not to pursue.
George played this in the first and second season of Grey's Anatomy - he was in love with Meredith, who spent the time pining over her married ex-boyfriend and sleeping with anyone she met at a sleazy bar. Eventually they slept together, but she started crying in the middle. It kinda didn't go too well.
Crais is interested in Aeryn in Farscape, and it takes her a long time to realise that's why Crichton's acting like a two-year-old around him. Of course, the fact that Crais continually called her "Officer Sun" is probably one of the reasons it didn't occur to her that he was interested in that way.
In ER, Ray was this towards Neela. In the end, they are seen together. Another case would be Romano and his friend Dr Corday.
For at least 7 episodes during the first season of Glee, Emma plays the hopeless suitor to the seemingly oblivious Will.
And Karofsky to Kurt in the second and third seasons.
Friends: Gunther had an obvious longtime crush on Rachel, but she never even knew about his feelings until the last season and the entire audience knew that she was going to be with Ross in the end.
Moriyama towards Tenkaichi in The Conditions Of Great Detectives who loves the attention but ignores how honest her feelings out. Banzo tells her every single episode that she isn't his love interest, Fujii is.
Gossip Girl is currently playing this straight with Dan and Blair. Blair (as always) is in love with Chuck. She treats Dan like her closest friend and confidante, and even ships him with her friend (and his ex) Serena, apparently oblivious to the fact that he's been in love with her for half a season.
C.C. Babcock, Maxwell Sheffield's business partner on The Nanny, wanted him to be with her rather than Fran Fine. However, she does get together with Niles, Maxwell's butler in the end.
Pushing Daisies: Poor Olive never stood a chance with Ned once Chuck appeared on the scene.
Very briefly on The Big Bang Theory, Raj to Penny. The reasons are a little complicated, Penny was having dinner at Sheldon's apartment with Raj and, because Sheldon can be hard to be around, was drinking a little too much. Sheldon went to bed and while she continued talking with Raj she confessed she still had feelings for Leonard but he was now taken in a very serious relationship. The combination of alcohol and both feeling romantically frustrated ended with them waking up in bed together the next morning. Raj interpreted it as him being Penny's "#2" after Leonard in the social group, while she was too embarrassed and apologized for leading him on. Unusual for the trope once the dust settles Penny and Raj do become closer friends.
Baby Gat from Noah's Arc relentlessly pursues Noah, particularly in the movie (to no avail).
Jonathan, Jack Donaghy's assistant on 30 Rock, is hopelessly obsessed with Jack and devoted to him.
Funnily enough, the same actor who plays Jonathan, Maulik Pancholy, plays Sanjay on Weeds and is similarly obsessed with Nancy.
Elaborated into an entire episode of How I Met Your Mother, crossing into Master of the Mixed Message. It referred to letting someone be on your "hook" where (intentionally or not) you allow someone to be enamored with you and you gather all the benefits of an ego-booster without having to commit to them, sometimes sprucing up your dialogue with "I can't be with you... right now." Ted was doing this by accident to a girl at the university library, and when he realized a girl was giving him the runaround too he sought to make things right with her. In a more long-term issue, Lily's high school boyfriend Scooter has shown up throughout the series and has made it clear he wants her back.
Joy Mercer on House of Anubis is this for Fabian Rutter, having liked him for at least a year BEFORE Nina even knew Fabian. [[spoilers:even AFTER Nina leaves, Fabian still turns her down, and rather rudely too.]]
Damon on The Vampire Diaries. He never gets the girl and the girls always seem to choose his brother Stefan over him. Damon does not have much luck in the romance department.
Helen Chao in Flower Drum Song. Wang Ta does get her in the Dream Ballet, but when he's awake he gives her no reason not to reprise "Love, Look Away."
Akiha in the canon Tsukihime ending. Shiki will generally notice that all the girls around him are attractive, except for Akiha, as she's his adoptive sister. Akiha tends to respond very poorly to all his love interests except Hisui, not just Arcueid.
Although she doesn't seem to mind Sion in the sequel game Melty Blood, possibly because, of all the girls that fall for Shiki, he shows less romantic interest in her than any other heroine (except Satchin).
In Duel Savior Destiny the main character's new best friend Selbium is constantly trying to get together with Mia, but whether she's aware or not (she probably is) it's pretty clear that it's never going to happen. She's clearly much more interested in jumping her brother's bones despite his disinterest.
In Homestuck, Eridan continues trying to go after Feferi even after she rejects him and starts a relationship with Sollux. To complicate matters, Eridan also begins to desire a blackrom relationship with Sollux because of it. Both are unrequited. It doesn't end well.
Also, Nepeta's crush on Karkat, who is in love with Terezi and later Jade.
There's also Roxy's crushes on both Dirk and Jake: Dirk is gay from the outset and interested in Jake, who already has enough on his plate figuring out how to handle Dirk and Jane.
Also, there's Kanaya's crush on Vriska, who is exclusively into Tavros (and later John) and who never sees Kanaya as any more than a faithful Morality Pet. In case it's not obvious, Homestuck is very dedicated to the All Love Is Unrequited trope.
In an odd example, Nocturne fails to romance Scribble Quill... and then discovers that ladies of other species take an intense liking to him.
Linkara has had it bad for The Nostalgia Chick ever since she pretended to sleep with him. He puts her on a pedestal and encourages her distaste for responsibility by blaming her stalkage of Todd on Todd himself.
Sissi, who is crushing on Ulrich. However, even after losing his memory in one episode, Ulrich can't stand Sissi and would much rather be with Yumi.
Johnny, who has an all-too-blatant crush on Yumi. However, she'd rather be with Ulrich (and besides, Johnny is a little young for her). Hiroki (Yumi's little brother) even tells his friend how little chance he has with Ulrich around.
A minor version is Milly's affections towards Ulrich, only shown in a few episodes. Considering she is two or three years younger, that is why she was never considered a serious threat. The show really did dance around the Love Dodecahedron.
Rogue had this going on with Cyclops in X-Men Evolution; it's not entirely clear whether he ever actually realized she had a hopeless crush on him, but in any case his feelings for Jean (even before they officially got together) made it a moot point.
Liz Allen in The Spectacular Spider-Man managed to hook up with Peter, but it was clear from the start that Peter's always had feelings for Gwen. Inevitably Peter dumps her to be with Gwen, causing her to hate his guts again. But seeing as the series ends with him unable to hook up with Gwen due to Gwen dating Harry now, it seems Liz is having the last laugh.
A minor case in an episode of Danny Phantom has Valerie being pursued by a geek named Nathan, a situation she is not in favor of. Of course, she ends up dating Danny briefly instead.
Meng, a young girl with a crush on Aang. Aang doesn't notice this and spends much of said episode trying to woo Katara. He knows eventually, but he gives her the Just Friends speech, one she accepted...in public.