The protagonist of Heir to the Throne, Konrad, is a prince and rightful heir-to-the-throne who fights alongside his troops in their struggle against the usurper Queen Asheivere. Subverted when it's revealed that Konrad isn't the real Prince Konrad, but an orphan that Delfador raises to overthrow the tyrannical queen.
The founder of Wesnoth, Haldric, spends his campaign The Rise of Wesnoth as a prince, even though his father King Eldaric IV of Stormvale dies early on until he establishes Wesnoth and becomes its king. Like every campaign protagonist, he takes part in all of the battles in the campaign.
Bladed Fury has its heroine, Princess Ji Jiang of China during the Warring States, who kicks plenty of ass using assorted weapons. She's on a quest to stop an evil minister from summoning supernatural forces to conquer China after all, besides rescuing her elder sister from demons.
Chest: Zong is the Prince of the Nether, wields a sword, has Nether magic, and is the strongest party member by far.
In Crusader Kings 2 your ruler automatically joins your commander roster, along with your marshal and your appointed commanders. Leading battles is dangerous though, and can get your ruler killed. But sometimes this is exactly what you need.
If you are a high-ranked ruler (usually Grand-Duke or higher) the majority of your appointed commanders and your marshal will probably be landed nobles anyways, since rulers are usually better leaders than courtiers, due to better education, war or hunting focus and character modifiers.
The most prominent example in the entire franchise is Gwyn, the Lord of Sunlight. As the ruler of mankind, he led his Silver Knights into battle in the war against the everlasting dragons, and his lightning spears were key to mankind's victory as they pierced the Nigh-Invulnerable scales of the dragons.
The titular king of the Dark Souls II DLC Crown of the Ivory King was the strongest knight in the land of Forossa (a land of Proud Warrior Race Guys known for their savagery on the battlefield) before becoming the king of Eleum Loyce, and was always the first to swing his sword in the defence of his kingdom and his people. Upon discovering the gateway to the Old Chaos he had a cathedral built around it and acted as the first line of defence until he sensed the degradation of his own soul, at which point he gathered his best knights, left the kingdom to his queen and threw himself into the Old Chaos to contain it.
Yhorm the Giant in Dark Souls III is described as having been one before becoming a Lord of Cinder. His ancestors had been ruthless conquerors but when the people his forefathers had subjugated asked for his aid in a war he led them into battle, protecting them behind his enormous shield.
Lorian, also of Dark Souls III, shows up in full armour, unlike his scholarly brother Lothric, and killed a Demon Prince. Unfortunately for him, the brothers' shared curse has rendered Lorian mute and possibly severely brain-damaged, although he and Lothric are still a Dark Souls boss fight, and so will essentially be difficult enough that you could build horseshoes out of them.
The Dancer of the Boreal Valley, once a princess of a distant line from the throne, was apparently skilled enough with blades that Pontiff Sulyvahn gave her swords modelled after his own before conscripting her into the Outrider Knights. Unfortunately for both her and you, the Outrider Knights were a large-scale Uriah Gambit in which Sulyvahn exiled people who were inconvenient for him to go fight other countries and outfitted them with magical Body Horror rings so they wouldn't come back, meaning that your response on seeing her is likely to be less "what a badass princess" and more "oh god oh god it moves so quickly why is this game so hard".
Prince Ariona Allant, aka Ostrava, from Demon's Souls counts, but it's stretched a bit as he needs rescuing two of the three times you meet him in the Boletarian Palace.
King Cailan of Dragon Age: Origins fits this trope... at least in his mind. He's particularly eager to battle the Darkspawn at the side of the Grey Wardens, like the kings featured in old stories, and is never seen out of his massive suit of GOLD battle armour. Unfortunately, his first encounter with an Ogre doesn't go well for him.
Then there's his half-brother Alistair, your fellow Grey Warden. Since he's a party member, he's considerably better at it and if he takes the throne, he even gives the rallying speech before the Battle of Denerim.
If you take the Dwarven Noble Origin, you briefly held the position of Commander of Orzammar's army before events force you to be exiled and join the Wardens.
The Human Noble has shades of this, as does their family. It's even more the case if a male Human Noble marries Queen Anora and becomes Prince-Consort, or if a female Human Noble romances Alistair and puts him on the throne, becoming Queen-Consort. In Awakening, they have to cut their honeymoon period short and return to active duty as the new Warden-Commander of Ferelden.
In the Awakening expansion, when a new Darkspawn threat emerges in Amarathine, the Warden (newly promoted to Warden-Commander) is made the new Arl of Amaranthine in order to combat the threat of the Darkspawn and rebuild the Arling in the wake of the Blight.
Similarly in Awakening, Nathaniel Howe has elements of this, attempting to redeem his family's sullied name.
In Dragon Age II, Prince Sebastian Vael of Starkhaven, whose family was murdered and throne usurped, leaving him in exile. Depending on Hawke's relationship with him, he can be convinced to return to Starkhaven and retake the throne.
Over the course of Dragon Age II, Hawke becomes a noble in Kirkwall, the city's Champion, and, depending on whether or not they support the Templars, can even become the new Viscount/ess at the end of the game.
While the Qunari do not believe in royalty, the Arishok's entire role as defined by the Qun could be considered this. Even the title "Arishok" can be variably translated as "One who struggles" or "Person of War".
The Prince of Midenhall, who is your party's most powerful physical fighter, literally jumps from his throne and sets off on a quest to defeat Hargon when he hears Moonbrooke has been destroyed.
The Prince of Cannock, albeit his skill issplit between fighting and magic.
The Princess of Moonbrooke is the party's weakest fighter but she is a good mage.
Dragon Quest IV: Alena, the Tsarevna of Zamoksva and the strongest physical fighter among the playable characters.
Dragon Quest V: Unlike his father, Parry was born and raised as a prince, however he's also spent pretty much all of his life fighting and it shows.
The Prince of Somnia in Dragon Quest VI. He leads the group that destroys all 4 Dread Fiends and the Archfiend, is the only person alive who can equip the legendary artifacts, and is able to unlock the 'Hero' class much more easily than any other character, only needing to complete one of the four prerequisite classes.
Dragon Quest VII: As the true son of Sharkeye and Anais, the Hero Auster inherits his mother's royal line.
Male heirs who are old enough, which in a monarchical government style are princes, can be brought in as generals for armies in Europa Universalis.
The heroine of the Beat 'em Up game An Egyptian Tale is the Pharaoh's daughter and a warrior princess fighting an evil cult worshipping Anubis, who is responsible for her father's death. She gets to slice up over a hundred enemies throughout multiple stages, culminating in a final showdown with Anubis himself.
EXTRAPOWER: Sharkungo isn't just the Stare Lore champion, he's also Prince of the Shakun Star and doesn't hesitate to fight when the Dark Force army invades his planet.
Edge in Final Fantasy IV, not counting the warrior kings in other games. Also, Edward, for a given value of "warrior".
Every playable character except for Bartz/Butz in Final Fantasy V, and several of the other main and secondary characters. Honestly, any royalty in FFV that isn't a Warrior Prince/Princess is being mind-controlled by the Big Bad. Lenna and Krile in particular are a mix of this and Rebellious Princess. Faris/Sarisa zig-zags it a hair, though, as she's both not wholly aware of what she is at the start, and then is not really comfortable resuming her old position once it's discovered, having grown used to the life of a pirate.
Final Fantasy VI gives us Sabin, a powerful Monk and twin brother of King Edgar of Figaro.
Ashe from Final Fantasy XII she's actually waaaaaaay more efficient when she does NOT have troops to command. There's also Larsa, the young Prince of Archadia who joins your party at times and is quite a useful party member.
Noctis from Final Fantasy XV definitely counts, as he destroys whole platoons of soldiers to defend his kingdom and the crystals. As may his love interest Luna, although she might be more of a Lady of War.
Fire Emblem has more warrior dukes and marquesses than anything, but it doesn't lack warrior princes:
Fire Emblem: Genealogy of the Holy War: The second part of the game has the sword-fighting Prince Leif of Thracianote Who would get his own spotlight game in Fire Emblem: Thracia 776, whose quest involves reclaiming his homeland from evil king Travant, and the swordsman Prince Shannan of the fallen Isaach, as well as Prince Lewyn the wind mage of Silesse, whose dead body the dragon Forseti is possessing...plus the Evil Prince half-brother of the main protagonist, Prince Julius the dark mage of the Loptrian Empire. Finally, there's main protagonist Seliph. He's in a weird place where he's technically a duke (of the fallen duchy of Chalphy in Grannvale), but being the firstborn (and rightful) son of the last descendant of the royal family also makes him a prince.
Fire Emblem: The Sacred Stones: Twins Prince Ephraim of Renais (whose side of the story has him learning that he cannot solve everything with fighting) and Princess Eirika (who learns she can't solve everything with diplomacy). Most of the other main characters are royalty of their respective nations.
Fire Emblem: Awakening: Prince Chrom of Ylisse, who's introduced as the leader of a small vigilante group known as "the Shepherds" and midway through the game becomes the Exalt/King of Ylisse. Lucina, being Chrom's daughter from the Bad Future also counts as a warrior princess (though in her timeline, it's implied Ylisse was overrun by Risen and destroyed and she makes no claim to it when she comes to the past because of the infant version of herself that already exists there takes precedence) and even the Avatar themselves, technically, especially if specced for a more combat heavy role, since their father Validar becomes King of Plegia after Gangrel's defeat, though this isn't really touched upon in the story. If a female Avatar marries Chrom, you get a whole family of Warrior Princes and Princesses, since this will mean the Avatar's son Morgan becomes a Prince too.
Fire Emblem Fates has four warrior princes in the spotlight. In Hoshido, there's Ryoma and Takumi, who are a Master Swordsman and archer, respectively. In Nohr, there's Xander and Leo. Then there's the Avatar, who can be the prince of both nations. Any of these characters' male children are also this by default. The Female Avatar's child, Kana, stands out in particular due to being the prince of three nations, Hoshido, Nohr, and Valla.
Fire Emblem: Three Houses has Dimitri, crown prince of the Holy Kingdom of Faerghus, as the straightest example. Claude, heir to the leading house of the Leicester Alliance, is one in function, and he's also a straight example since he's the crown prince of Almyra. Edelgard, crown princess of the Adrestian Empire, and Petra, crown princess of Brigid, are gender inversions. All of them fight on the front lines.
Fire Emblem Heroes introduces siblings Alfonse and Sharena, royalty of the kingdom of Askr, as well as members of the Order of Heroes on the frontlines of battle.
Game Master Plus: On the Fighter route, Elsa can recruit Lasse, a prince of Gardeth, as a party member who can wield axes and has a combination of offense and support skills.
Quite a lot of people in Heroes of Might and Magic, in both 'verses. Archibald and Roland Ironfist are probably worth mentioning for being the first clear ones (canonically Roland more — Archibald fought in the siege of his final stronghold for the final battle while Roland served as a Hero for his top field commander during the final battle, but it would have been the other way around if Archibald had won the war).
Though they never call him by the "prince" title, Jak from Jak and Daxter still fits the bill due to his royal heritage.
King Mickey can save you in the hard boss battles and is basically the Yoda of the Kingdom Hearts series.
Kairi is one of the seven Princesses of Heart, but also wields the Keyblade and is one of if not the strongest non-Sora playable character in the Re Mind scenario of Kingdom Hearts III.
Princess Amelie, a demi-god princess, from King's Bounty will go to another dimension with only her skills and a pet dragon to gather a mighty army that can liberate her kingdom from marauding demons in King's Bounty: Armored Princess
King Graham in King's Quest; justified in the fact that he was a knight before becoming king. Alexander may also count — although he's not really one for physical confrontation or battle, he's still accomplished some pretty badass feats, including quickly mastering many magical spells and riding Death's horse into the land of the dead.
Princess Naree from Krut: The Mythic Wings, a princess of the Garuda tribe and a capable fighter on her own. She first appears as a Mini-Boss in the Garuda stage, and after a Defeat Means Respect moment, she then joins your campaign, where she serves as a Frontline General for her men.
Legend of Heroes is a game set in Ancient China, where the Tang Dynasty Princess, Falan, uncovers an invasion plot and leads her three best soldiers to defeat the enemy forces before they can strike.
Another female example: Princess Zelda is shown in such a capacity in the flashback sequence of The Legend of Zelda: Twilight Princess. She combines it with Lady of War when she helps Link in the game's final battle.
Prince Sidon of the Zora from The Legend of Zelda: Breath of the Wild. Years before the beginning of the game, he defended the fishers of Hateno Bay from a giant Octorok by stabbing through its innards when it swallowed him. During the main plot, he has Link ride on his back while the latter fires Shock Arrows at Divine Beast Vah Ruta. It's also mentioned (and shown in Hyrule Warriors: Age of Calamity) that his late older sister Mipha was an even greater warrior than him.
All of them in Hyrule Warriors. Zelda, Ruto, and Midna are three princesses of defined kingdoms who are not afraid to fight on the front lines, risking life and limb to save their world. Agitha, although not of royal descent, is the self-proclaimed princess of the insect kingdom, and she too is willing to get her hands dirty to save Hyrule.
Mortal Kombat has Goro who is prince of the Shokan race, General of Outworld's armies, and 9-time champion of Mortal Kombat.
The water controling Rain the purple ninja is a Prince... get it? Though he is a particularly dickish example believing his heritage to Edenia gives him the right to rule Outworld with an iron fist. No wonder he and Goro get along.
Kotal Khan was technically a prince for a time though Shao Khan conquered his people, Kotal is so badass he is one who taught the Aztecs how to be brutal (oh and he has sun powers). However, unlike Goro and Rain, Kotal does care for the citizens of Outworld and becomes their ruler after Mileena proved unsuitable.
Kitana is the princess of Edenia and a skilled fighter and assassin. In the original and rebooted timelines of the games, she led a rebellion to free Edenia from Shao Kahn's tyranny.
Prince Tristan in the first and the second Ogre Battle games.
You control Prince Rhys of Landen in Phantasy Star III, and since the game is a Generational Saga, his future son and grandson are also princes in their playable time periods.
The Prince of Persia. Ironically, the main character of Sands of Time is a prince by blood; the other protagonists just happen to have this title as a nickname, while the main character of Prince of Persia becomes a Prince by marrying a Princess at the end. Ditto for Dastan in The Movie, even though he's an adopted prince. Played completely straight for his older brothers, who all have royal blood. The eldest brother commands the army. The second brother leads the cavalry, while Dastan has a special squad perfect for infiltrating fortifications.
Suikoden V series features a benevolent example in the Prince of Falena, the Silent Protagonist of the game, while Suikoden II features the evil variety in the Prince of Highland, Luca Blight.
In Tales of the Abyss you have a warrior Princess in Natalia Luzu Kimlasca Lanvaldear, the heir apparent of the Kingdom of Kimlasca-Lanvaldear. She's one of (if not, by end game, the absolute best) the greatest archers in the world and uses her archery skills to protect her people. Technically, Luke and by extension Asch is set to become the prince-consort of Kimlasca-Lanvaldear when Natalia ascends, as she intends to take him as her husband.
In Tales of Graces, you have Richard, Prince and later King of Windor. While he prefers diplomacy, Richard is not against getting dirty to aid his people.
In Tales of Zestiria, Alisha Diphda functions as a warrior princess. Interestingly, due to the fact she was not the first child in the family, she has virtually no hope of actually becoming Queen of Hyland, so she specifically sets out and uses her nobility to help her people in whatever way she can, especially if it involves using a spear.
In Total War, as your generals are all members of your royal family, this is commonplace.
New Legends have you playing as Prince Sun-Soo of the Soo Kingdom (loosely based on the Ming Dynasty) and a capable fighter trying to reclaim your throne from a cruel tyrant who enslaved your people.
Prince Gilgamesh from The Tower of Druaga. Major bonus points for being able to climb up a tower, kill every monster in said tower, destroy the evil demon Druaga, save his lover Ki, and then go back down the tower!
Varian Wrynn as well as his son Anduin Wrynn (the latter using magic).
Jaina Proudmoore, daughter of Lord Admiral Daelin Proudmoore (who also uses magic)
Garrosh Hellscream, son of Warchief Grom Hellscream.
Taelia Fordragon, daughter of Highlord Bolvar Fordragon (in Shadowlands — Fordragon was never properly a faction leader until he took leadership of the Ebon Blade after Sylvanas shattered the Helm of Domination and freed him from the Frozen Throne. He merely served as a regent during Classic because the aforementioned Anduin was too young to rule.
Moira Bronzebeard, daughter of King Magni Bronzebeard (who also uses magic).
Artos who becomes the 'Warrior King' in the single-player campaign for the computer game Warrior Kings. He starts off as the son of a powerful baron and when his dad is murdered at the command of the Big Bad of the game, Artos leads an uprising and conquers province after province eventually owning the entire empire in the name of vengeance and either scientific enlightenment, the One God or the tribal gods of the pagans. Artos is very much the picture of Rank Scales with Asskicking: barring the demons, the big bad, and his 2nd, there is no unit more powerful than Artos and that's before he gains increased stats and new powers.
Bart from Xenogears appears to be a pirate, but is really a prince in hiding.
Barbarian (Titus): Keela is a warrior princess who has taken upon herself a mission to kill an Evil Sorcerer who among other misdeeds nearly destroyed her father's domain.
Twin Goddesses Nina and Syllin, the co-protagonists of the game, shortly after the murder of their father, the king, take it upon themselves to reclaim their family's domain.
