In Black Cat, Saya is Train's Not Love Interest. Her function in the plot is similar to that of a traditional dead lover / love interest; in fact, Train's affection for her is enough to cause Creed to "take drastic measures". But it's later revealed, perfectly and seriously, that Train never contemplated any romantic involvement with her.
Before the Eclipse, Guts and Griffith of Berserk were very much like this. Griffith in particular took things to rather Yandere levels, particularly as he started falling further and further toward the Despair Event Horizon. Before Guts, Griffith was also the most important man in Casca's life as well. He tends to have that kind of effect on people.
In Bleach, Ichigo rushes into the unknown to save Rukia from Soul Society, and later does the same for Orihime, rushing into Hueco Mundo to save her. Neither girl is his official Love Interest.
In Naruto, Naruto is somewhat attached to Sasuke, even after he leaves Konoha to join Orochimaru, then goes rogue and basically becomes an international criminal. Before then, the show devotes not insignificant amounts of time to the two rivaling each other at becoming better ninja; both is (partly) the other's inspiration. However, Sasuke is not as much Naruto's friend as Naruto would like him to be.
Tenchi and Kiyone of Tenchi Muyo! often drift into this kind of relationship, notable because she's one of the few regular female characters not infatuated with him.
Kiyone does drop that she might be interested in Tenchi in Tokyo to Ryoko and Mihoshi, saying that Tenchi could use a more serious, down-to-earth girl like Kiyone (and really, it's hard to blame her). Though, given the context of the scene, she could have been saying it just to push Ryoko's buttons.
An interesting case in Eyeshield 21: at the beginning of the series AnezakiMamori initially joined the football club for the sake of Sena, her childhood friend, arguably most important person at the time, and Not Love Interest. More specifically, she joined to protect him from the bullying of the football club’s captain, HirumaYoichi. Initially, Sena is all Mamori cared about, getting worried over his injuries and yelling at Hiruma for picking on him and etc. However, as the series progressed, Mamori started spending more time with and getting closer to...the aforementioned Hiruma Yoichi. It got to such a point that at the end of the manga, although Sena is still a dear friend to her, Mamori completely intends for her and Hiruma to play seriously and defeat him, since he's on a rival team now. So while Sena remains the Not Love Interest and important to Mamori, it's hinted that at the end of the day, sticking by Hiruma is higher on her priority list.
In the TV series of Record of Lodoss War, Spark becomes highly commited to his mission to save Neese, as he's the leader of the group. It's even made fun of by Leaf and Raina, who put quite an effort into getting them together. In the end it seems he only manages to rescue her with The Power of Love, but once she is freed from the dark magic and awakens in his arms, she just hugs him in thank and there's never any indication that Spark wasn't just trying to protect a good friend.
Rune Soldier, which is based on a work by the same author as Record of Lodoss War, does it again with Louie and Melissa. At first Melissa is devestated by being ordered by her god to support unlikely hero Louie as a "Valliant Champion", as he is the complete opposite of what she always hoped for. Over the course of the show, she helps Louie to overcome some of his worst traits and comes to appreciate his genuinely good nature and desire to help people in need. Over time, she stops being constantly embarrased by having him as her valliant champion and even stands up to others to defend him against being called a useless idiot. While there are certainly some scenes with heavy romantic overtones between them, they never show any actual romantic interest for each other, and it's heavily implied that Ila is actually Louies girlfriend and has been so for quite some time before he met Melissa.
Despite several characters making jokes and comments about it, Setsuna and Marina of Gundam 00 genuinely seem to not have any romantic interest in each other. Their connection comes more from the fact that they are from neighboring countries and are both searching (in very different ways) for answers to the same questions. When outright asked if they were dating, they both deadpanned "We are not a couple" in unison, without any of the embarrassment or blushing this kind of situation usually entails. If anything, their relationship is more akin to that between a mother and child.
This is Riff and Cain's relationship in Godchild. Cain has a number of Love Interests over the course of the series — and they all have a noticeable impact on him — but Riff is the person with whom all his trust and strongest feelings lie. And Cain is the only significant person in Riff's entire life.It's played around with quite a bit towards series end, though arguably The Grand Finale managed to play the trope straight once more.
Cassian and is this to Jezebel, though the latter only acknowledges Cassian as being the "one who saved him'' moments before dying in his arms.
What Doumeki from xxxHOLiC can potentially be considered to Watanuki. Early on it was determined the two of them would have some sort of connection and practically everyone around them in-story was Ship Teasing them (and so were the fans). They also wind up doing a number of Heroic Sacrifices for each other, Doumeki especially. But at no point does Doumeki ever explicitly express any romantic interest to Watanuki, and Watanuki never fully gets over his distaste for Doumeki. Also, for the first half of the series Watanuki's intensely crushing on his classmate Himawari, and then spends the rest of the series pining after his boss Yuuko for the next 100 years after she dies, and ultimately Doumeki's married to someone else.
Case Closed provides a rather odd example. Ran and Conan enjoy hanging out together, look out for one another, and generally are very close. The dub even has Sonoko make a joke about Ran being Mrs. Robinson to Conan, bringing him somewhere as a "date". The strange part comes in that Conan is also Shinichi, who is Ran's love interest. She has no idea of that though, only thinking of Conan as a child, so it's this trope from her perspective.
In MegamindIntrepid Reporter Roxie Ritchie is always being saved by superhero Metro Man and is quite emotional when he's no longer there to protect the city. However, it turns out they were never actually involved, to the surprise of Megamind (Roxie's realLove Interest).
Wreck-It Ralph gives us an interesting (and rather Squick-ish) example: Vanellope von Schweetz. The movie takes place within the worlds of several video games where the characters' sizes vary, and fans who only saw Vanellope's character design mistook her for an extremely short adult. Naturally it was assumed that she was the Love Interest of the title character Ralph, until her voice actress Sarah Silverman revealed that the character is nine. Vanellope and Ralph form a very close sibling-like relationship in the movie, although it can be said that if Vanellope had been old enough the story might have been different. Note that neither character is human, so she'll be nine forever.
Finding Nemo has Dory, a blue-tang fish with short-term memory loss who befriends Marlin the clownfish on his quest to find his son. Most of the movie consists of their dialogue with each other, they share body contact often, and even though she's not attentive most of the time she truly worries for him. Yet they never hook up, probably because 1.) interspecies dating is really weird, and 2.) Marlin's a widower who lost his clownfish wife to a barracuda, and most likely is in too rough a time of his life to find another wife.
Word Of God (aka Audio Commentary) states that Dory was introduced to serve as a surrogate child so Marlin could re-adapt his parenting approach.
In The Road to El Dorado, Miguel and Tulio are each other's Not Love Interests—not only do they hide their friendship by fighting, confess how much they mean to one another as they think that they're slowly dying, but they even have a painful break-up! According to some, the original script had them more explicitly be lovers—no wonder their Ho Yay factor is so high.
Film - Live Action
Danny is this to Nicholas in Hot Fuzz. Word Of God says that in the original script Nicholas had an actual love interest, but she was cut and some of her storyline and actual lines were given to Danny.
The previous page picture◊ is from the Doom movie, which took a certain pleasure in subverting the typical hero/heroine love interest angle, as well as other tropes. Samantha and John Grimm are estranged but loving fraternal twins.
In the remake House Of Wax 2005, the characters played by Elisha Cuthbert and Chad Michael Murray seem very much like ex-lovers who will reconcile at the end, since everyone else is dead. But they're brother and sister, so no.
Barney and Sandra in The Expendables. He ultimately decides to return to Vilena with his crew and rescue her, but it's because he respects her courage in standing up to the Big Bad, not because he's fallen in love with her.
Ariadne and Dom in Inception. The latter is still a little hung up on his deceased wife and the former gets some Ship Tease with Arthur, and there's a tiny bit of an age gap too.
Calvin and Spooner's relationship in I, Robot shows all the classic signs of them becoming love interests — even a Scar Survey — but by the end, there's nothing to suggest they're going to be more than friends.
Star Wars: Leia is this to Luke Skywalker. He's fixated with rescuing her from the moment he sees her, she's the one who's name he screams when he is dangling off a Bespin tower, she's his main confidant and comforter, and threatening to turn her to the Dark Side is his Berserk Button. She's his sister, natch. Of course...other people have interpreted their relationship inotherways.
Snow and Emilie in Lockout. The former is sent on a mission to save the latter when she is held hostage onboard a giant orbital space prison. The two bicker and banter and Snow basically acts like a jerk towards her the whole time, but they grow to genuinely care for each other. The epilogue when they arrive back on earth teases a romance and includes an almost-Almost Kiss, but the movie ends with them still just friends.
In the film adaptations of both The Da Vinci Code and Angels and Demons, the love interest aspect of the female leads Sophie and Vittoria are removed, when they were quite present in the books. In The Da Vinci Code, Robert is kind of an uncle figure/protective older brother to Sophie, and in Angels and Demons he and Vittoria are pretty much strictly business. Tom Hanks explains that the frantic pace of the plot of the latter led the filmmakers to excise the romantic subplot.
Quorra to Sam in TRON Legacy. She rescues him, they battle together and defend each, she confides to him her desire to see a real sunrise, and the two sometimes have awkwardly cute moments with each other. At the end of the film, though, Quorra and Sam are not dating: a deliberate choice by her actress Olivia Wilde, who knew such a romance would feel unbelievable.
Hawkeye for Black Widow in The Avengers. He's the main reason she joins the team, but they're never shown to be anything beyond extremely close friends.
Even after Harry Potter fell in love with Ginny Weasley, their romance always took a backseat to his friendship with Ron; indeed, Harry almost never began dating Ginny in out of fear that it would tick Ron off. Hermione also takes this role sometimes — notably when the trio were separated in The Deathly Hallows.
Arguably Luna. She was the only one who could successfully comfort Harry after the death of Sirius, and the two later went to a dance together in what was legitimately Not A Date. Word Of God even notes that Harry's friendship with her (as well as Neville) is meant to mark his Character Development between books five and six.
This is quite likely the case between Frodo and Sam in The Lord of the Rings. There's obviously strong affection and emotion between the two, and incredible devotion, especially on Sam's side, but in the end Sam winds up marrying Rosie Cotton and becoming mayor of the Shire.
Merry and Éowyn. He's devoted to her, treats respectfully and commends her courage when everyone else puts down her desire to fight in battle, and the two even kill the Witch-King together. However, Éowyn ends up hooking up with Faramir.
The Chronicles of Vladimir Tod, Henry and Vlad. The two are extremely close and often act more like love interests than any of the girls (many girls, in Henry's case) that they are interested in. Vlad seems to be Henry's only serious relationship.
In The Dresden Files, Harry's relationship like Thomas is like this sometimes. Thomas Raith the incubus is Harry's friend and half-brother and they never have any doubts about the relationship, but when Harry is between girlfriends, Thomas takes on that role in the story a little bit: He's closer to earth in some ways and has needed to be rescued more than once.
Although Harry does pretend to be"Toe-moss"'sgay lover once, to keep someone from questioning why he was searching Thomas's apartment (since nobody else knows that they're half-brothers)
Because Sherlock Holmes isn't that close to his brother Mycroft and eschews the possibility of friendships and romantic interests as things that might get in his way, Dr. Watson is literally the only important person in his life. It's shown most clearly in The Three Garridebs when Watson is wounded, but it's apparent in subtler ways throughout the series. For his part, Watson, despite being a more emotional and social person than Holmes, has few friends, no surviving family, and is unmarried or a widower for most of the series, so that Holmes is the most important person to him.
The Meg Cabot novel Teen Idol is all about a small town girl who has to show a glamorous movie star around her high school while he's preparing for a role. The movie star kick starts the plot, helps her start to come out of her shell and gain some confidence, the two develop a close relationship, he takes her to prom, and then...they both hook up with other people. The Just Friends excuse they were using throughout the book was genuine.
Tal and Milla, the two leads of The Seventh Tower, are this to each other. A boy and a girl, both decently good looking and about the same age (teenagers at that!), whose relationship forms the emotional backbone of the series and who start out hating each other but gradually develop an incredibly strong rapport- and they never make the slightest move towards getting together romantically. Tal at one point admits that Milla is pretty (albeit after another character brings the subject up, and he admits to have not really given it much thought before that) but that's as far as he takes it; Milla never even goes that far. The (admittedly small) fandom still ships them sometimes, though, and neither has an actual Love Interest.
Live Action TV
In Body of Proof, Peter is this for the lead character of Megan Hunt. Despite them both being straight, single, and non-family type of partners in a crime-solving drama, there is no hint of them being anything more than friends and co-workers. The writers pull it off quite successfully with very few people passionately shipping them.
They slipped in a scene in Sneeze when Clark and Chloe went to the beach (offscreen/post-episode). By themselves. They actually invited Lois to come along but she declined.
And that phone call in Beast. It is just so fitting for a superhero and the love interest who is sacrificing herself for him (not to mention they had a suspiciously similar in-universe fictional superhero Warrior Angel that had pretty much the same thing, Action).
Joey and Phoebe in Friends. Also a Fan Preferred Couple and often hinting about potentially being together in a future. Besides some isolated kisses, they never actually dated, never had sex and in fact Joey ends up introducing Phoebe to her husband to-be. Lisa Kudrow and Matt Le Blanc even wanted to throw in a line during Phoebe's wedding episode that implied the two had been having casual sex throughout the show's run. But the producers denied them.
Also Joey and Chandler (referenced in the Joey spin-off).
NCIS: Tony and Ziva have drinks, dinner, spend time together... but it's Not A Date. Ditto for McGee and Abby (who are exes), Gibbs and Jenny/Ducky... the show seems to run on this trope. The team's become so co-dependent and attached to one another they seem to function as each other's love interests.
It sometimes seems like any woman Xander dates is doomed to play second fiddle to the two very important women in his life, Buffy and Willow. Cordelia senses it ("When you're not babbling about poor, defenseless Willow, you are raving about the all-powerful Buffy"), and Anya seems to as well ("When things get tough, he/ Just hides behind his Buffy"), hence her fight with Willow in "Triangle" (An imperfect example because both women were in fact love interests for him, but in Willow's case it was only briefly.)
For that matter Buffy serves as The Not-Love Interest for Willow. After Tara's death, before she embarks on her quest for vengeance, Willow visits Buffy; who was shot, and saves her life.
Elsewhere in the Buffyverse, when Spike appears in Angel season 5, he quickly takes on a role like this, as their complicated history and relationship drives a lot of drama, far more than anything to do with Angel's actual love interest for the season. Again it's noted by Joss on the DVDs. "We finally found the right girl for Angel - Spike." Hilariously, the in-universe movie adaptation of After the Fall, called "Last Angel in Hell", gender-flips Spike into Angel's love interest.
In season four Angel's son Connor filled this role.
Mal and Zoe. One episode centers around Wash's complaints that there's UST between them. However, at the end of the episode Mal and Zoe's attempted kiss (to "defuse" this so-called tension) is painfully awkward. Even the resident BadassJayne, normally the most lecherous member of the crew, is unnerved.
Zoe: [dead monotone] Take me, sir. Take me hard.
Jayne: Now somethin' about that is just downright unsettlin'.
So much so that they inspired the first Slash Fic.
Roddenberry himself declared about a romantic relationship: "...we certainly believe that the affection was sufficient for that, if that were the particular style of the 23rd century." Draw your own conclusions.
Played more straight in the new movie, with Kirk and Spock re-enacting the basic pride and prejudice hate-turns-into-love story...only platonically. Damion Lindelof (producer) even commented on the DVD that the heart of the story was Kirk and Spock "falling in love with each other, in a way, but not in a romantic way, in a Butch and Sundance way."
Monk's closest relationship is with his nurse Sharona and later on her replacement Natalie. They are not romantically involved. Given that they were inspired by Holmes and Watson, it's a given.
House and Wilson in House, given that they're based on Holmes and Watson. Wilson is, if not the most important person in House's life, damn close. He's also the only person House seems to genuinely care about.
The US version of Queer As Folk has Michael Novotny and Brian Kinney. While they don't get the explicit romantic pairing of their British counterparts, it's clear that they're it for each other. Twinks come and go, husbands and children and family are important, but when it comes down to it, the comic-book addicted geek and the slutboi-with-issues are the love story of the show.
M*A*S*H: Hawkeye Pierce was a notorious casanova, but in the later seasons his relationship with BJ was his closest, to the point where their goodbye became the final scene and emotional climax of the entire series. Hawkeye flat out tells him he's the best friend he's ever had.
They have also gotten (platonically) jealous of each other's friendships with other men, from Hawkeye subtly distrusting Leo Bardanero in "Last Laugh" to BJ's ongoing jealousy of Trapper. They bicker like an old married couple and their REALLY intense fights ("Period of Adjustment," "Preventive Medicine") are WHAM episodes. They "get back together" before the rolling credits both times.
Tim and Daisy in Spaced. One of the series's main subplots is the slow-but-steady erosion of the "not" from the phrase. The last scene in the "Skip to the End" documentary demonstrates this, showing them as a couple with a child.
Chuck and Ellie (his sister) seem to do a lot more hugging than Chuck and Sarah in Chuck.
A good example of that was shown at the end of the season 5 episode the Santa Suit. Sarah had been captured and kept hostage by Shaw - a man that had vowed to kill her in the past to avenge the death of his wife - for the entirety of the episode. Once Chuck beats Shaw though, he runs over to give Ellie a hug rather than checking to make sure that Sarah, his wife, is alive and unharmed.
The Inspector Lynley Mysteries: No one will ever be as important to Thomas Lynley and Barbara Havers as they are to each other, to the point where they have explicitly called each other their reason to get up in the morning. Lynley's relationship with Helen consistently takes a backseat to his relationship with Barbara. If they're not in love with each other, they're this trope.
Wire in the Blood had Dr. Tony Hill and his Most Important Person DCI Carol Jordan. Seeing as Tony has difficulty being a real boy on the best of days, Carol kept him grounded and reminded him there was life outside work and serial killers.
Dr. Cal Lightman and Dr. Gillian Foster on Lie to Me, partners who own the Lightman Group and have serious Will They or Won't They? going on. Made explicit in "The Whole Truth", when Cal talks to the fiance of a man who engineered his own assisted suicide with the help of his best friend (named Leo):
Psych: Girlfriends may come and go, but Shawn and Gus will always be the most important people in each others lives. Though the hit slash pairing is Lassiter and Shawn.
President Jed Bartlet and Leo McGarry on The West Wing. They act and bicker exactly like an old married couple, spend all the time possible together, tease and flirt (in a joking way), and play a blatantly spousal/parental role in the staff's nuclear family-modeled True Companions. While Jed may have an excellent wife and family outside of the west wing of the White House, Leo is for all purposes the love interest in Jed's "other" family inside the west wing, with the thrill of politics in place of sex and romance.
On Dexter the titular vigilante has his sister Debra. He even notes in one episode that if he could have feelings for anyone, they would be for her.
However it's revealed that Debra has supressed feelings of the non-platonic kind in season 6 and later she admits it when Dexter gets a new love interest in season 7.
Mulder and Scully of The X-Files were this for each other from the get-go, and they were supposed to stay that way; the original idea was that they would never be more than platonic work partners. However, the chemistry between the actors caused their platonic relationship to look pretty non-platonic in the eyes of the fans, and by season five, the writers started playing with the idea that they could be more than friends. By season seven, they were.
If the writers genuinely never intended for there to be any Unresolved Sexual Tension between the two, then it was a bit of a Relationship Writing Fumble for Scully to show up at Mulder's place, still wet from a shower, and strip to her underwear so he could check her lower back for alien marks. This was in the very first episode.
Tori and Andre from Victorious. Made more interesting that they've done two love duets but they're best friends, and don't see each other as anything more. The only real moment of Ship Tease between the two resulted from Andre's crush on another character, which had Tori dress up and pretend to be the other character and that only results in an Almost Kiss.
Austin & Ally write songs alone with each other that are often romantic in nature, they share personal secrets, are constantly standing up for each other, get crowning moments of heartwarming every episode. They would be a textbook Disney style Just Friends pairing if it wasn't for the fact they Anchored Ship in the 3rd episode.
Eureka has Sheriff Carter and his Deputy Jo Lupo, but instead of a romance developing with those two, Carter ends up being involved with Doctor Blake.
Kurt Hummel from Glee has a perfectly good boyfriend to whom he is devoted, in the form of Blaine, but his father Burt will always, always be more important than anybody else in his life, especially after Burt's heart attack.
Kurt also has another one in his "BrassyHag" Mercedes. They're always there for each other, they do basically everything together, they're incredibly close...but Kurt just happens to be gay and not interested. Early in the first season, though, Mercedes was none the wiser and actually thought they were going out, until Kurt turned her down and later came out to her.
The same could be said for the duo in Elementary. Now portrayed as a woman, many viewers expected them to be paired together. They share a very close bond, are near inseparable, and live in the same apartment..But Word Of God is they will not fall for each other, and shippers aside they do not seem attracted to each other outside the norm for Sherlock and Watson.
The Doctor has this kind of dynamic with the majority of his companions. Especially notable are Sarah Jane Smith from the classic show, Donna Noble and the Tenth Doctor in New Series 4, and (once the ship was sunk) the Eleventh Doctor with Amy Pond & Rory Williams. He even went so far as to call them "the people I LOVE!!!" in one episode.
Up until around early season 8, Clark Kent and Chloe Sullivan, to the point where real-world journalists who hadn't kept up with the series assumed they were a couple in Season 6.
Skins had this with Emily and JJ in the latter's S3 episode. They helped each other overcome their problems and became close friends and, at the end of the episode, they even slept together. However, Emily made it clear from the beginning that it was a pity screw, simply a response to JJ's earlier statement that if he got to be normal for a day, the first thing he'd do was lose his virginity. The viewers know it's not going anywhere since, like the Kurt/Mercedes example above, Emily just isn't into boysthat way.
Wallace to Veronica Mars. Of course Executive Meddling said it would never happen. Weevil and Dick could also qualify as the same. Actually anybody but Troy, Duncan, Logan, and Piz could qualify
In The Sentinel, Blair Sandburg serves as this for Jim Ellison, serving as a support to deal with Jim's physical and emotional problems as a Sentinel and also needing Jim to rescue him every other episode.
In Warehouse 13 You have Pete and Myka, in a show like this normally the two main characters have UST, but Pete and Myka have purely platonic feelings for each other and don't think of each other in a sexual way, which Myka states in one episode after they think they had sex.
Babylon 5: Ivanova's relationship with most of the male leadership of the station can be described as a form of very affectionate professionalism.
Mark and Roger from RENT. Exemplified by the fact that the big reconciliation after Roger leaves New York for Santa Fe, and then comes back is not between Roger and his girlfriend, Mimi - it's Roger and Mark, who get an entire song ("What You Own") dueting about how similarly-miserable and yet still devoted to each other they are.
Several in BIONICLE, in part due to most characters being asexual and aromantic. For example, Gali tends to fill this role for Tahu, as she often argues with him and he is more protective of her than the other Toa. The two address each other as "brother" and "sister", although, this doesn't stop the shippers since they're Not Blood Siblings.
Otacon is Solid Snake's Not Love Interest in Metal Gear. In the first MGS, they have what could be described as a Meet Cute in a warped sort of way, exchange some emotionally loaded dialogue, and, if Meryl (the actual love interest) dies, Snake leaves with Otacon instead. And then they wind up raising a kid together in Metal Gear Solid 4.
The voice actors have some fun with how "Not" Otacon actually is (see the lengthy MGS entry under Ho Yay). In canon, though, MGS4 tried to sink the Snake/Otacon ship and make it clear he was the Not Love Interest and Snake's Platonic Most Important Person. Itdidn't work.
And Meryl counts, too. Even though she canonically survives, she never does become Snake's love interest. Hell, she actually hooks up with the series' dedicated Butt Monkey!
Rui to Wes in Pokemon Colosseum. Their initial meeting certainly seems like it's working up to a Rescue Romance, as Wes saves Rui from a band of kidnappers. The two team up, and Rui follows Wes everywhere. Without Rui's ability to see Shadow Pokemon, there isn't much Wes can do, so they depend heavily on each other. However, after that, there's not much evidence that their relationship is anything but platonic. Even the end of the game (which the Genre Savvy viewer might expect to hold some kind of Love Confession) has... not much, really. Maybe Rui's just not into bad boys. Though it's hard to establish any kind of a relationship when Wes never says anything.
Similarly, in the "This is not a Meet Cute" department, there's Double H to Jade in Beyond Good And Evil. After Double H's rescue, he becomes Jade's loyal sidekick, following her everywhere. His single-sided devotion to her slowly deepens to a real friendship between the two of them. However, there's no overt romance between them, though they are frequently shipped.
Kumatora to Duster (or maybe it's the other way around) in Mother 3. When Duster gets Easy Amnesia for three years), it's Kumatora who stays with him throughout it, even if only on the sidelines. And while she hides herself behind harsh words, she genuinely seems to care for him. But as for love? There's no real evidence of that.
Yosuke to the Protagonist in Persona 4, along with considerable amounts of accompanying Ho Yay.
It's very possible to have one of these in Dragon Age: Origins. Alistair and Morrigan are the most obvious ones, provided you're outside of their preferred gender, but pretty much anyone in your party can become this.
In the City Elf origin, Shianni serves this role for the protagonist. She's given a lot more characterisation that the Player Character's bride/groom and she shares more emotional dialogue with him/her, leading one to infer that the only reason she's not the love interest is because she's supposed to be one of their many cousins.
Dragon Age II follows suit with Aveline and Varric, who both cannot be romanced. Although the game actually does go out of the way to Ship Tease Aveline and Hawke (if the player chooses) before sinking that ship.
Varric however does once or twice admit that he considers a female Hawke to be beautiful. Word Of God has mentioned they originally thought about including a scene where an unromanced Hawke would have met up with Varric at the end, revealing the two were in a secret relationship.
Final Fantasy XIII-2 has this with Noel and Serah. They have basically the same dynamic as any other male and female lead of a JRPG, but Serah is engaged to Snow, and Noel has Ship Tease with Yeul.
Miles Edgeworth to Phoenix Wright in Ace Attorney. Old childhood friend, troubled past, Edgeworth's frozen prosecutor heart melted by Phoenix's honest passion...it's no surprise they're the most common ship in the fandom.
At the same time, Maya Fey, the second most popular shipping option. She and Phoenix go everywhere together, they clearly care deeply about each other, and he often has to rescue her from some danger. But when someone suggests they're a couple, they respond with confusion.
In Silent Hill Downpour Murphy and Anne. The way she acts antagonistically to him because she mistakenly believes he killed her father can come off almost like she was a furious, hurt ex. In fact, in one lets play the player believed that Anne would be revealed as Murphy's ex-wife who left him for getting into prison.
Eruca in Radiant Historia. She and Stocke have a Lady and Knight relationship that's disproportionately close for how long they've known each other, he's constantly going through hell and high water to help and protect her, and they even get mistaken for a couple a few times. He's actually her older brother, so that would be a bit awkward. Hence, not much shipping from this one.
Kyousuke for Riki in Little Busters. It's constantly impressed on the audience how very close they are (often to ambiguously romantic levels), he gets an incredible amount of focus - though he doesn't have his own route, he's absolutely integral to Rin's route and gets even more plot focus in Refrain - and one of the biggest subplots in the game is the way their relationship changes over the events of the game, from friends to fighting to becoming even better friends. It's even more noticeable since this is Bishoujo game, which tend to have only minimal male characters and even more minimal character development for them. He's even alone among male characters in a Key Visual Arts game in having his own Leitmotif, something usually restricted to only the love interests.
In Virtue's Last Reward, Phi is the first girl that Sigma meets. They initially have a belligerent relationship, her ending is the True Ending of the game, and she has a lot of plot relevance... but she and Sigma are never even hinted to move in a romantic direction. At best, they go from Teeth-Clenched Teamwork to something resembling friends. Although there are some scenes with them when you fail to defuse the bombs, they're not exceedingly romantic. Word Of God has also confirmed that the two will never be a couple at any point.
Davan: Am I going to have carve "Davan loves you very much" backwards into your forehead? PeeJee: No, I think I got it this time.
In Red String, Ayu has been Makoto's best friend since they were little. She's easily the closest person to him since his beloved grandmother's death. There are absolutely no romantic feelings between them, despite what the fandom who wants him out of the way for Kazuo and Miharu might suggest.
Gwen to Ben in Ben 10. They are of opposite genders, but they're also cousins (not that that stops some people). Their relationship hovers somewhere between siblings, best friends, best frenemies, and everything else, all at once. While Gwen does get a love interest in the sequel series, Ben and Gwen are still #1 Best Teammates.
It's much more apparent in Alien Force since both characters have matured greatly, rarely fight, and openly hug each other
Oddly enough, Ben is also this trope for Kevin (who's love interest is actually Gwen, despite how close the two act sometimes.
Alan Burnett had plans where Dana, Terry's on-off girlfriend, would finally break up with him for good and have Terry start dating Max. Bruce Timm vetoed it with as much force as possible.
In The Batman, Batgirl and Robin are tweens/early teens at best and the two display almost zero romantic interest in each other, instead bickering and playing off each other as a brother and sister would, with a healthy dose of competition over who's the better sidekick thrown in.
Despite having a history together (As well as being the primary Transformers Animated turn-on) Blackarachnia always came second to Optimus in terms of importance when compared to Sentinel. He leaves the fembot behind behind to save Sentinel and himself which results in her transformation to technorganic, gets more episodes devoted to their rivalry, and in BA's last appearance he seemed more concerned about Sentinel than her. The ironic thing about this? The she-spider was the reason for their antagonist rivalry in the first place!
On Teen Titans, while Terra is Beast Boy's official Love Interest in season two, his teammate Raven fits this trope for the rest of the show, with the two sharing several close moments in relation to both of their character arcs. They're a Fan Preferred Couple and became canon in the DCU right around the time the show ended.
Some fans see this with Raven and Robin, who also share a few unusually close moments.
This is mostly what Ren and Stimpy's relationship in the original series is about. In the adult spinoff called Adult Party Cartoon, however, they are quite explictly portrayed as a homosexual couple.
On Daria, Daria and Jane have this sort of relationship. The final episode (not counting the finale movie) has Daria note this while Jane helps her through an emotional crisis:
Oddly enough Princess Bubblegum herself could be seen this way in more recent episodes. Finn may have some lingering feelings for her, but has decided to move on and is currently dating Flame Princess. Bubblegum is still the main female character on the show, though, as well as Finn's close friend and the princess he works the most with.
Gravity Falls: Dipper and Mabel Pines. No matter what, their loyalties lie with each other and harming one triggers the other's Berserk Button. Though there is some focus on Dipper's crush on Wendy, it's clear he values his sister's happiness first.