Haseo and Atoli in the final volume of .hack//G.U.+, fighting against Cubia together using their Avatars. Ditto for Kuhn and Pi.
Toru and Julie in Absolute Duo. Their school uses a special Duo system in which students are assigned figthing partners. Toru handles the defense with his shield, while Julie handles the offense with her dual blades. They will do anything to protect each other. And did we mention their Duo oath sounds like wedding vows?
Haru and Kuroyukihime from Accel World. In the OVAs, they have developed good battle combos and even merge together to give Kuroyukihime the ability to fly.
All You Need Is Kill: In the manga and Light Novel, Keiji Kiriya and Rita Vrataski fight together in the final battle, and then fight each other.
Deunan and Briareos from Appleseed. The couple gained attention for their combat prowess, and were recruited into an anti-terrorism unit together.
Ross Sylibus and Naomi Armitage in Armitage III. They are police and their romance is a plot point.
Krista and Ymir from Attack on Titan have shades of this, especially during a climatic battle outside the Walls. They launch into battle together, with Krista declaring she won't fear anything as long as Ymir is with her. Word of Gay confirms Ymir's romantic feelings, while Krista's remain slightly more ambiguous.
Nice and Jacuzzi are co-leaders of their bootlegging/explosives making gang.
Eventually, Claire and Chane; he proposed to her while they were fighting a mafia hitman on top of a train.
Elfin and Preyas from Bakugan, complete with Belligerent Sexual Tension and Cannot Spit It Out. They constantly argue about which one of them is Marucho's guardian, as well as other things, but when the time to fight comes, they make a great team. Whatever you do, do not, repeat, NOT attack Elfin, or else Preyas will go Ax-Crazy on you.
Basara has pirate leader Chacha and her lover and first mate Zaki.
Saya Otonashi and Haji from Blood+ have been fighting chiroptera together for decades, though they don't admit their feelings for one another until the finale.
Cardcaptor Sakura: Sakura and Syaoran Li start out as rivals, but fall in love during the second season. Syaoran decides to stay in Japan so he can help Sakura transform the Clow Cards into Sakura cards. On another note, Meiling would like to be this with Syaoran and they work well together but she's an Unlucky Childhood Friend.
In the End of the manga of Claymore, Raki has become a strong fighter, and it is strongly suggested that he and Clare eventually become a couple.
Dauf and Riful also qualify for this. They met when they were both warriors, Dauf fell in love immediately, and Riful liked him at least. Perhaps they soon became a love couple. Later, however, they are seen only as Awakened Beings, which is why it is more a case of Unholy Matrimony.
Kiri and Elraine in Double Arts. They even developed the TitlularDouble Arts fighting style to fight while constantly connected. They are the official couple of their series and will never let go of each other. No matter what. Elraine is afflicted with a special disease that killed a third of the world's population, and the only reason she isn't dead yet is because of Kiri's mysterious ability.
Happens eventually in Dragon Ball Z, when Gohan as Great Saiya-Man is joined by his girlfriend Videl as Great Saiya-Man 2 (called Great Saiya-Woman in the US). Their relationship is reflected in their In the Name of the Moon speeches.
Eureka and Renton's preferred method of fighting is piloting their shared mech while holding hands.
Also, Ray and Charles Beams are a more conventional example of this trope than Renton and Eureka. Instead of holding hands, they watch each other's back in a fight.
Yaoi Genre example: Dee Laytner and Randy "Ryo" McLean from FAKE. Both of them are highly-skilled policemen from New York, and both can fight very well.
Saito and Louise from The Familiar of Zero used to be the page image for Sword and Sorcerer. That alone should tell you about how awesome a Battle Couple they are. Similar to the Negima example, Louise summoned Saito to be a warrior/bodyguard for her in battle.
Freezing has this as the main premise, with an older female Pandora and a younger male supporter called a Limiter. One of their abilities, the "Ereinbar Set", specifically requires that the Pandora and Limiter have a relationship based on deep, mutual trust. It's not so surprising then that, as Violet mentions, many Pandoras end up marrying their Limiters. As per the trope, these couples are particularly vulnerable to losing one half during battle (they fight Eldritch Abominations, after all), and the manga does show the psychological and social effects of losing a partner in combat.
Roy and his bodyguard Riza are this in all but name, since the biggest obstacle to a Relationship Upgrade is something out of their reach (anti-fraternization laws in the military). Their mutual feelings are more or less clear, however, plus in the manga and in Brotherhood they get a scene that screams this: when Roy is blinded after being forced to open the Gate and Riza is greatly weakened after barely surviving a Slashed Throat, they manage to remain in the war game by having Riza guide and correct Roy's aim, letting her keep on fighting and allowing him to keep using his powers despite his lack of sight.
Yuki and Yuno qualify as this after they finish with the 7th; she's the heavy hitter while he's The Strategist.
Ai and Marco (the couple that comprises the 7th) qualify as this as well. That's their gimmick, after all.
Renais and Soldat J from GaoGaiGar. They may or may not be "official" but they do get a power up when they hold hands and undeniably work as an amazing team.
Ghost in the Shell: They would both deny it until the day they die, but the Major and Batou of Public Security Section Nine definitely fall into this trope. Even their voice actors agree that the series is in part, a romantic story.
Badass Normal Pip Bernadotte and Friendly Neighborhood Vampire Seras Victoria. Even more so after Pip dies and Seras drinks his blood to become a true vampire, absorbing his soul. The resulting carnage is both terrifying and epic.
Alucard and Integra. The scene of them in the middle of the last battle was epic; and then she shoots the Major while he is fighting Walter. They are an Official Couple, according to Word Of God.
Inuyasha and Kagome have the Guys Smash, Girls Shoot dynamic; Kagome often will ride piggyback like an archer on horseback.
Miroku and Sango, eventually, form a more Back-to-Back Badasses couple; her demon fighting skill and his holy power is a formidable combination. They effectively subvert the Guys Smash, Girls Shoot trope, as both of them have long range (Sango's Hiraikotsu and Miroku's Wind Tunnel) and short range (Sango's sword and Miroku's staff) attacks.
Inukami!: Youko would like to be this with Keita, and from the perspective of EVERYONE ELSE they are. From his perspective she's just his demon busting assistant.
Kenichi: The Mightiest Disciple has Kenichi and Miu, who, due to having sparred together for a long period of time, naturally fall into this slot whenever they have to fight side by side.
Hiroshi and Miwa in Kotetsu Jeeg, to a degree: she's more of an Ace Pilot than an Action Girl, but she is the one who must deliver the parts of Jeeg itself as Hiroshi transforms into its head and then puts them all together.
Max and Milia/Miriya from Macross/Robotech are probably one of the earliest examples in anime. Their races were at war. Max is a human, and Milia is a Zentradi, but after she defects, the two end up marrying and Milia gets a red variable fighter to match her husband's blue one. They even lead different squadrons together for a time span of about 30 years after the events of the original Super Dimension Fortress Macross.
Fate and Nanoha are actually something of an subversion. Being in separate branches of the TSAB and having very different jobs (Nanoha as a Combat Instructor in the Air Force and Fate as an Enforcer in the Dimensional Navy) means that they're rarely in the same place at the same time while on active duty. Nanoha even points during the first battle in StrikerS that it's been a long time since they've fought side by side.
Erio and Caro from Magical Girl Lyrical Nanoha Strikers. While other ships had fought together, they're the two that are rarely seen in battle without the other. They're also a lot more dependent on each other than the other pairs; Caro powers up Erio and serves as the primary transportation, while Erio handles the actual combat. Finally, they're one of the few couples that's official, rather than just loads of Ship Tease. They also double as a Sibling Team (both were adopted by Fate, but they didn't meet each other until they were ten).
Mahou Sensei Negima!. Generally speaking, the setting requires something like this because most mages are squishy and need a physical-fighting warrior to protect them. It was invented to be practical more than anything, but Negi says two Pactio partners often end up marrying each other. Because of this, the Pactio system has heavy romantic undertones in magical society, though we are shown several examples of non-romantic Pactios. Character-specific examples of this are:
Negi and his partner Asuna; he's the mage and she's his athletic and protective fighter. Interestingly for this trope, Negi decided to train as a Magic Knight so he wouldn't have to rely on and put her in danger as much.
Taki Reizen and Klaus von Wolfenstadt of Maiden Rose are a Boys Love example since Taki is a powerful commander in his country's army, Klaus is his also very badass "personalknight", and they kick copious amounts of ass either separately or when they fight together.
When Kouji and Sayaka get Put on a Bus in Great Mazinger, Kouji's adoptive older siblings Tetsuya Tsurugi and Jun Honou pick up the mantle and continue with the tradition, fighting together in the titular Great Mazinger and in Venus-A respectively.
Duke and Hikaru eventually become this in UFO Robo Grendizer. At first Duke fought alone in Grendizer, but later Hikaru went through an Adrenaline MakeoverandTook a Level in Badass, piloting one of the companion shuttles that help Duke out in battle later (the other two are piloted by Duke's friend Kouji and Duke's sister Maria Grace.)
Mobile Suit Gundam 00: Allelujah Haptism and Soma Peries/Marie Parfacy, after Marie returns to action in the GN Archer, which combines with Allelujah's Arios Gundam to form the Arios Archer. In The Movie, they co-pilot Gundam Harute.
Mobile Suit Victory Gundam: Renda de Baroma and Duker Iku are an anti villainous example. Both are skilled pilots and rather fearsome in the battlefield, not to mention pretty high-ranked members of the Zanscare Empire, and they hope to settle down in peace when the war's over. And to finish the war, they'll fight our heroes. After they both kick it in battle, their souls are seen riding together in a Harley-like motorcycle to the afterlife.
The first Hokage (Hashirama) and his wife (Mito) are Implied to be this, considering she was the original Jinchuuriki of the Nine-Tails and Kushina's Old Master.
Minato Namikaze and Kushina Uzumaki were this, which is proved when they come up with an awesome and heartbreaking Thanatos Gambit to seal the Nine-Tails inside Naruto at the cost of their lives, so they can save Naruto's life and their village.
Iruka's parents are mentioned to have been this, though they died when Kurama was unleashed.
Naruto becomes this with Hinata in the canon movie The Last: Naruto the Movie. Naruto's own chakra has no effect on Toneri, and the only way to cause harm comes from the specific chakra that Hinata obtained from Hamura Otsutsuki. However, Hinata's own chakra levels are not strong enough to stop Toneri on her own. So by Holding Hands, Naruto and Hinata share and combine their unique chakra to defeat and destroy Toneri's Weapon of Mass Destruction, by combining Naruto's Rasengan with Hinata's Eight Trigrams Twin Lions Crumbling Attack.
Sasuke becomes this with Sakura in Naruto Gaiden. When their daughter Sarada is threatened, they both spring into action. Messing with two-thirds of the Second Coming of the Legendary Sannin was a bad idea on Shin's part.
Neon Genesis Evangelion Shinji and Asuka at their best. The episode "Both of You, Dance Like You Want to Win" sees them undergo syncronization training so they can fight like this against a double angel. It involves a great deal of personal bonding in addition to combat training. It is reinforced in Super Robot Wars, where they are given combination attacks when they show up: as seenright here.
Girls Love (sorta) example: Noir, with Kirika and Mireille. Chloewanted to have Kirika as her partner and it almost works, but then she attacked Mireille...
Oscar and Andi from the Pokémon anime are a spoof of the trope. They are efficient as a team-up (and the same goes to their Nidoqueen and Nidoking), but they also are huge Shippers On Deck who claim to be able to spot couples in love a mile away and thus try to hitch Ash with May and Jessie with James.
You'd thinkRanma and Akane would be one of these but that is often not the case. For starters, Akane's typically a bystander in any battles Ranma gets involved in — if she isn't back at home while Ranma's out in the middle of nowhere beating on whoever's ticked him off, she's sitting on the sidelines and watching while he does all the fighting... or is hypnotized, kidnapped, tied up, or turned into a doll and otherwise incapable of joining in. When Akane does join in the fight against an opponent, assuming she and Ranma fight the same foe, they tend to get in each other's way more than anything (or, at least, Akane herself is overwhelmed and Ranma has to pull her fat out of the fire). This is because Akaneresents the way Ranma assumes "I'm the greater martial artist, so I gotta protect Akane", which typically leaves them wide open to the exploits of their enemies. The one exception in the series, the one time they really pulled the Battle Couple deal off, was during their face-off against the Orochi. There's a reason why Rakaneshippers in particular like to see that story as THEIR best moment in the whole series.
The best time they had good synergy, which was even recognized by the audience, was during Martial Arts Cheerleading. When Ranma wasn't even aware that he was supporting Akane who was wearing a mask.
Ranma also fights alongside his other fiancees, Shampoo and Ukyo, several times throughout the series.
Tsukune Aono and Moka Akashiya from Rosario + Vampire are gradually developing into one of these, as Tsukune starts to develop the powers necessary to fight at or near her level. Fong Fong's parents are one as well, and in a recent chapter Yukari and Fong Fong himself are hinted at becoming one (they haven't officially gotten together, but it's pretty strongly hintednote The epilogue even more strongly hints that they will get together in the future. and they've got the teamwork down pat).
Tsukune and Moka have been deified for it.
Sailor Moon: One would think Sailor Moon herself and Tuxedo Kamen would be this, being the main characters, but this trope instead goes to Sailor Uranus and Sailor Neptune, who arrive together and usually attack in tandem. The former couple do fight as a unit once in a while, and in the Sailor Moon S anime their strong bond is what allows her to get the first of her Mid Season Upgrades, but despite his efforts Tuxedo Kamen isn't up to par with Sailor Moon as much in the first anime.
Senki Zesshou Symphogear: Kirika and Shirabe from their introduction in Symphogear G are always together, forming a lesbian couple and perfectly complementing each other in battle.
The incestuous Aizel siblings have a similar dynamic; "Love for himself" Sorath does the Leeroy Jenkins style attacking while "Love for others" Tiriel pulls power of existence from another location to heal him.
Soul Eater: This trope is a common fandom interpretation of the meister-weapon partnerships. Shipping aside, canon does nothing to dissuade this whatever yourpairing preferences in most cases. The only truly canon pairing of this nature is Maka's parents; her father was her mother's Weapon. As of the end of the series Marie being pregnant with Stein's child would suggest they are the second canon example.
Kirito and Asuna become one in the first arc of Sword Art Online. Specially impressive in the anime, where seeing them fighting together, coordinating their attacks, is truly spectacular. Although it gets played down in the later arcs, as most of the stories usually keep them apart (most of the times, focusing on Kirito, although Asuna gets to be focus instead in the "Mother's Rosario" arc). However, whenever they do battle together, expect much pure, unadulterated awesomeness.
Kamina and Youko; she watches and protects his back while he takes the front for one battle.
Simon and Nia are co-pilots in Gurren Lagann's final form in the climax.
Leite, who does all the maintenance (being in the direct war zone) while hers truly, Makken, is in the battlefield.
Tenyori Mo Hoshi Yori Mo has a more subdued example in Mio and Shou, who use their powers in tandem in the Grand Finale but focus less on fighting evil and more in protecting the city of Kamakura from being consumed by fire, an earthquake, and ultimately a tsunami. They succeed, but then they go the Together in Death way.
Almost all the series that form the Time Bokan franchise, save for Ippatsuman and Yattodetaman, feature a battle couple as the leads. The better known ones are Tanpei and Junko from the original series, and Gan "Gan-chan" Takada and Ai "Ai-chan" Kaminari from Yatterman.
Now that they have been indirectly confirmed, Tsubasa -RESERVoir CHRoNiCLE-'s Kurogane and Fai. They always fight together even at the start of the story and have a knowledge of the other's fighting style that is astonishing. Even with their problems during the Infinity Arc they're still back-to-back.
Twin Star Exorcists is the title given to a married exorcist couple whose child will be The Miko, in this case Rokuro and Benio. While the two are more than a little bit against the couple idea, there's no denying that together they make an awesome team.