KaoriYanase was a finalist in the previous two tournaments. but was defeated both times by Reimi. So it's become her personal goal to surpass Reimi's skill.
But the series' most strained relationship, is the one between Chiho Masuda and her cousin, Kyoko Kirishima. They used to be close, but Chiho's decision to desert their Clan has driven a wedge between them. Kyoko has been ordered to find her wayward cousin and either capture her, or kill her if she refuses to comply. She defeats Chiho, but chooses to let her go.
There are many rivalries from the Advance Wars series between COs (Commanding Officers). Eagle and Andy (one of the missions where you fight Eagle is even named "Rivals!"), Sami and Sonja and possibly Grit and Max from the first game, Adder and Sensei and Lash and Sonja from the second game, and possibly Hawke and Candy/Kindle from the third. Days of Ruin/Dark Conflict doesn't have rivalries as such; everybody generally just hates each other, except for the NRA and IDS (the two main antagonist armies of the game) who get along nicely. Except when in a reveal the player finds out that Caulder/Stolos (the Mad Scientist and Big Bad) couldn't really care less about anyone living or dying (the NRA included), apart from when it has "scientific" purposes, and essentially leaves the NRA to crumble after its defeat.
Originally it was Knuckles. In his debut, Knuckles fought against Sonic and Tails due to manipulations by Dr. Eggman. After Eggman revealed himself as the Big Bad, Knuckles teams up with the duo to stop him. Afterward, probably due to their egos, Sonic and Knuckles clashed for one reason or another, mostly due to the latter being tricked by Eggman into doing so. Their rivalry has kind of dissipated in recent years due to other adversaries showing up and Knuckles becoming more of an ally, but still pops up now and then.
Since Sonic and Knuckles were slowly becoming friends, Shadow debuted as the new, darker rival for Sonic. Unlike Knuckles, Shadow was not being tricked into fighting the heroes and was in fact a dangerous foe in his debut. Originally, he didn't pay Sonic much attention outside of accusing him of copying his style, but due to Sonic's tenacity and cheating death, he earned Shadow's respect and acknowledgment as a Worthy Opponent. Even after Shadow's eventual HeelFace Turn, this dynamic is retained and the two clash quite often before teaming up against a common foe.
Debuting alongside Shadow was Rouge the Bat, who served as The Rival to Knuckles. They're both treasure hunters, but it's more of a hobby for Knuckles and he guards the all-powerful Master Emerald instead, while Rouge is an outright thief who attempts to steal it. This dynamic tends to be laced with Foe Romantic Subtext, though.
In the Mega Man (Classic) series, Bass is Mega Man's rival, obsessed with proving his superiority over Mega Man.
The most famous one is between the series' two resident Ninjas, Sub-Zero and Scorpion.
While Sonya Blade has one with Kano they act more like archenemies, She and Frost have a rivalry against each other, but neither character has ever explained why.
Kitana has one against her Evil Twin Mileena, while Jade has one against Tanya (who betrayed the royal family).
And as for friendly rivalries, there's Liu Kang and his fellow Shaolin Kung Lao.
Wario is Mario's rival, though it's doubtful whether Mario has noticed.
Waluigi is also supposed to be Luigi's rival. It's even less likely that Luigi has noticed.
Wario's actual rival is probably Captain Syrup, a villain in some games that he's starred in, whose greed is said to be even greater than his.
The Mario Party series portrays Donkey Kong and Bowser as rivals which explains why, in Mario Party 2, DK always goes for the Bowser Bomb (which summons Bowser to the board). Later games make them Foils by giving their spaces opposite functions: DK gives out Stars and coins while Bowser takes them away. On a similar note, DK himself may also act as a rival to Mario, depending on whether or not Nintendo feels like having him fulfill his (Grand)father's role.
In Onmyōji, Kyūmei-neko develops a rivalry with Seimei after the latter whupped her butt at the end of the first chapter only to have it repeatedly whupped again afterwards, even in a goddamn dream.
Kyūmei-neko:(after being defeated for the second time in a single episode) Turns out, I can't win after all, nyan.
In Darkstalkers, B.B. Hood doesn't intend on letting any of the creatures from Makai live, but the fighter she seems to hate the most is Lilith. In one of Hood's artworks, she and Lilith are hugging, but Hood is holding a gun to Lilith's head. In another, Lilith and Morrigan are in a house, and Lilith turns around with a scared expression, looking at B.B Hood's shadow; Hood is holding a knife.
Final Fantasy IV Has Cecil and Kain have been rivals since childhood but Kain eventually turns evil by Golbezs mind control, enabled by Kains negative emotions.
Final Fantasy VIII subverts the trope with Squall and Seifer. While Seifer does have a beef with Squall and sees him as his competition, Squall honestly couldn't care less about Seifer and would prefer not to be bothered with him. It's unknown whether Siefer fails to realize it, or simply doesn't care.
Final Fantasy XIII-2 has Lightning and Caius, as they are fighting against each over the goddess of death Etro, Lightning is fighting to protect the goddess, while Caius is trying to kill her to save a girl named Yuel.
Sora and Riku in Kingdom Hearts. They're friendly rivals throughout the whole series, but for most of the first game, Riku became distrusting of Sora and fought against him due to succumbing to the darkness, being manipulated by Maleficent and eventually possessed by Ansem. He spends the majority of the next few games atoning for it.
Hayner's and Seifer's gangs have a heated rivalry in II. Roxas and Seifer seem to have the strongest vendetta, although how much of it is simulated by DiZ's computer is unknown. The real Seifer also seems to have something against Sora, although he shows him a little more respect.
Guilty Gear: gives us Sol Badguy and Ky Kiske. Both were colleagues of the Sacred Order of Holy Knights that was created by Kliff during the Crusades. Sol and Ky while respected Kliff and each other strength, they both however disagreed with each other method. It started when Ky finds Sol stealing the Fireseal. Technically, he took it back because he was the one who created it along with the other Jinki/Outrage weapons. It then became a misunderstanding/clash of ideas. Sol owned Ky everytime though since he had more power and experience like day and night. By the end of Accent Core+, the rivalry became a lot more friendlier.
Mana Khemia: Alchemists of Al-Revis has Roxis to the main character Vayne. So much so, that on one occasion he even thinks of competing against Vayne in a marathon, even though they're on the same team.
Kirameki High, the High School of Tokimeki Memorial 1, has a sworn rivalry with Suega High, a neighbour High School, especially in sports domains (Suega's Soccer Club is known as one of the strongest in the National Inter High Circuit, and the opponent to reach and defeat for Kirameki's Soccer Club, in Gaiden GameNijiiro no Seishun ; it's also one of the last and strongest opponents in other sports clubs' friendly matches, in the original game) ; this doesn't prevent the two to cooperate and doing a common music concert in Tokimeki Memorial Pocket.
Kirameki High also has a sort of rivalry with Hibikino High, the High School of Tokimeki Memorial 2, but it is a much more friendlier one than the one with Suega High, as students from both High Schools interact a lot and often come to the other High School and their neighbouring districts.
Between individual characters:
Tokimeki Memorial 1 has Yumi and Saki, for the Unknown Rival variety (Yumi considers Saki her rival for the protagonist's heart as soon as Saki shares a bento with him, but Saki doesn't notice Yumi's jealousy ;
Tokimeki Memorial 2 has Mei and Homura, for the Arch-Enemy variety, as well as Junichiro and Takumi towards the protagonist, if they're in love with the same target girl as the protagonist, for the straight version of the trope.
Hanna and Linda are sworn rivals who don't get along and can go into Volleying Insults, but they hold each other in high regards, Hanna admitting Linda is a faster runner than her, and Linda going for the trouble of going to Dolphan Academy to discover her, and deep down admiring her perseverance, being herself a hard-worker.
The Asian and Johan, if the Asian goes for Sophia's heart, although the rivalry is anything but friendly, as Johan is not pleased by this.
In the House of the Dead franchise, James Taylor seems to share a friendly rivalry with Thomas Rogan, hinted by the vs CPU mode in the Typing of the Dead and James' comment in the final score screen in the House of the Dead 4.
Ulysses of Fallout: New Vegas is heavily implied to be this for The Courier, with them eventually having a final showdown in Lonesome Road. He's also a case of Unknown Rival in that the Courier has never heard of him prior to the DLC.
Kyo Kusanagi and Iori Yagami from The King of Fighters. Their rivalry has rooted since the times of their ancestor. Iori is COMPLETELY OBSESSED with wanting to kill Kyo, and while Kyo is usually dismissive, he wouldn't miss out a good brawl with Iori.
Riki is Kunio-kun's rival. In some games, such as Renegade or Crash N The Boys Street Challenge, he serves as a boss fight or foe.
Touhou has Marisa versus Reimu, and Marisa is/was (depending on whether you consider the events in PC-98 game as having happened) even a stereotypical enemy-turned-rival. There's also the considerably more violent Mokou versus Kaguya. Recently, Reimu has gained another rival in fellow miko Sanae, whose shrine is quite popular among the people of Gensokyo.
Rival Schools: Roy serves as Batsu's primary rival, which was initially fueled by Roy's contempt towards Japan, over what'd happened to his grandfather during WW2, and because Roy was an elitist due to coming from a wealthy family. By the conclusion of Project Justice, Roy's attitude towards the people of Japan had begun to change and he bagan competing with Batsu on friendlier terms.
Asura's Wrath: Yasha is Asura's main rival in the story mode. Akuma / Oni becomes an even better example in Lost Episode 2. Both Asura and Akuma are so determined to defeat each other, they turn into statues after fighting for over 500 YEARS! Then they start moving again, and fight even more!
Graves sees Twisted Fate as his archenemy. They were former con men and partners in crime many years ago, before Twisted Fate turned on Graves in exchange for great magical power. After escaping his confinement, Graves joined the League solely to get revenge on Twisted Fate.
Kassadin and Malzahar have it out for each other. Both have looked into the Void and received its power, but whereas Malzahar considers it a gift he needs to spread, Kassadin sees it as an abomination that must be destroyed. They have clashed both in the League and outside of it.
Zilean and Volibear don't seem to like each other at all. This is part of a Development Gag; the real-life Zilean, the design director for Riot games, once went on record saying there would never be an armored bear hero in the game. This sparked a forum war between those who supported armored bears, and those who didn't.
Sejuani sees Ashe as this. Both come from Frejord - a harsh tundra environment with precious few resources - and both from different tribes. Whereas Ashe is willing to play nice with both the League and Tryndamere's barbarians to bring peace to Frejord and increase her influence, Sejuani is a traditionalist who believes Might Makes Right and refuses to yield under Ashe's banner.
Viktor sees non-playable character Professor Stanwick as this, for stealing the credit of creating Blitzcrank and the technology used to revive Urgot.
Hecarim and Mordekaiser are implied to be this by some of the quotes given by the altars in the new Twisted Treeline.
In sega version of Lord Monarch Alfred have his rival, Gessyu, which he have to face him in Rubia's challenges.
The Dueling Mini-Game lets a player offer another player on the opposite team a duel. If the other player accepts, the entire server will be notified of their new-found rivalry, and the winner is the one who kills (or assists in killing) the other player more than vice versa.
In-universe, Scout and Heavy, Soldier and Demoman, and Spy and Sniper are confirmed rivalries among the classes. Redmond and Blutarch, the leaders of RED and BLU, have the most major one.
In Tekken, there are Paul to Kazuya, later Kuma to Paul, Kunimitsu to Yoshimitsu, Raven to Yoshimitsu, Dragunov to Raven, Hwoarang to Jin, Lily to Asuka, King II and Murduk until they become friends, Armor King II to King II. Yoshimitsu and Bryan also qualify, but they are rather Arch-Enemies to each other. There are also Sibling Rivalries, Nina and Anna, and Lee to Kazuya.
In Robopon, there's Bisco in the first game and Nick D. in the second.
In the Classic and Alpha series, every original character had a rival (doubling as a love interest) who could also be selected as the protagonist, reversing the roles. Among the originals, there's also Rai Branstein to Ryusei Date. Alpha 2 has Sleigh Presty to Ibis Douglas (and vice-versa) and Kukuru to Sanger Zonvolt. Baran Doban serves as a rival to both Sanger Zonvolt and selectable protagonist Touma in Alpha 3, and Spectra McCreedy for either Selena Recital or Viletta. In Advance, whichever of the two pilots (Axel Almer or Lamia Loveless) you don't select serves as a rival.
Sanger Zonvolt to WodanYmir, Yuuki Jagger to Bullet Luckfield, and Kyosuke Nanbu to Axel Almer in OG2. The ATX Team and SRX Team have a friendly, professional rivalry in OGs.
2nd Original Generation introduces a pair of antagonistic Choukijin pilots as rivals for the playable RyuKoOh and it's pilots, as well as the Argent-Class Boosted Children for Arado, Seolla and Latooni. Michiru Hanaten thinks of himself as a rival to Kohta Azuma. Aracari Garcia more-or-less fills this role for Sleigh Presty and Ibis Douglas, in addition to their established rivalry with each other. Throughout the series and in Masou Kishin, Shu Shirakawa is somewhere between rival and arch-enemy to Masaki Andoh. The Series has a lot of characters.
Bloody Roarsubverts this with Long. While he's said to be Yugo's rival, he doesn't care about competing with Yugo and would actually prefer not to (they're not exactly on good terms with each other). As far as Long's concerned, the acknowledgement is enough.
In Mighty No. 9, Ray is Beck's rival according to theWord of God. While both characters have the ability to absorb the Xel of other robots, Ray does it out of necessity due to being a deteriorating robot. Because of this, Ray is more of a loner than Beck.
There's usually at least one character in every game developed by Capcom's (now defunct) Clover Studios/PlatinumGames that acts as a rival to the main character(s) of the game, and in many cases:
Viewtiful Joe has plenty with "Another Joe", Alastor, Jet Black and Captain Blue all candidates.
There's a "hero vs. rival = red vs. blue" trope in Capcom/Platinum's rival lineup (Dante vs. Vergil, Viewtiful Joe vs. Captain Blue, Wonder-Red vs. Wonder-Blue). The Platinum crew is clearly aware of this and has even subverted the trope a few times.
The original Bayonetta featured "red vs. red" (Bayonetta vs. Jeanne), and Bayo 2 would have fully inverted the trope by changing Bayonetta's primary color to blue for "blue vs. red" if she and Jeanne hadn't become friends by that point.
Even in spite of his glowing, red eye when he lets his Super-Powered Alter Ego take over, Raiden in Revengeance is still more commonly associated with blue (given his lightning motif) than Sam, who has a red and black artificial arm and a sword with a crimson blade, fully inverting the trope.
A rival is a staple Recurring Element in the Tales Series, but Tales of Berseria puts a different spin on it. When you first meet him, Oscar Dragonia has all the trappings of the rival character: he's in charge of the Hellhole Prison the protagonist Velvet was trapped in, he's a subordinate of the Big Bad, and he fights her to a standstill during her escape in a battle you don't quite finish. After setting him up as someone who the party will be competing against for success, the game takes a hatchet to everything the player expects from a rival; he's a non-presence for most of the plot, and when he does appear, it's mostly so things can go From Bad to Worse for him. He ends up a villainous Failure Hero through and through, a complete non-entity to the party only appearing to Velvet with all the presence and memorability of a traffic cone.
Randal's Monday: Kramer to Randal. They're always at odds and have similar skill sets. Both are Deadpan Snarkers and both are experts at figuring things out (as Kramer is a detective and Randal is trying to unravel a Stable Time Loop).
The Scooby-Doo video game Scooby-Doo, Who's Watching Who? had the Mystery, Inc. gang competing with a rival team of paranormal sleuths on a reality show called Ghost Scene Investigation. The Ghost Scene Investigation team start out resenting Mystery, Inc. for overshadowing their popularity and constantly beating them to identifying the criminals disguised as ghosts.
In Colosseum: Road to Freedom the character Narcissus serves as a rival for the player character. Narcissus is in direct competition with the player to participate in the plan of the charming Marcia, and Narcissus detests the player for seemingly winning her over.
Alouette from Recettear: An Item Shop's Tale appears to be this to Recette in their initial encounter. However there are no game mechanics that actually have her compete against Recette, and in fact she will be your favorite customer as she buys at some of the highest percentages. The subversion is intentional since what Alouette really wants is a friend, not a rival.
A staple of the Stylish Action genre, with most of these rivals either mirroring the main character in moveset, or being the opposite in personality. Such examples include: