In Area 88, Saki Vashtal is an Asranian prince who also serves as an air force commander and Ace Pilot in Asran's civil war.
Bakugan: Fabia, the princess of Neathia, is one of the Battle Brawlers in the main team. Fittingly enough, her debut season, Gundalian Invaders, involves a war between the Neathians and the Gundalians.
Lelouch from qualifies, despite being an exiled prince. He commands Japanese rebels to battle against the Holy Empire of Britannia, and he enters the battle himself while he orders his army to do the rest. It fits his mantra of "If the king doesn't lead, how can he expect his subordinates to follow?" and he even manages to pin Cornelia down at the Battle of Narita.
Said Princess Cornelia li Britannia is a Lady of War and Commander-in-Chief of the Britannian military. Among the Britannian forces, only Suzaku is a better pilot.
Prince Schneizel commands the Britannian military as well, and he leads soldiers on the battlefield as efficiently as if he were looking down upon a chessboard.
This is expected of Britannian royals. Princess Cornelia and Prince Schneizel, both prime examples, looked down on their half-brother Clovis because he refused to become this, being a sensitive painter instead. This pressure is why he decided to become viceroy, even though he was not cut out for it.
To illustrate how much this is expected: it could be said that the reason Lelouch and his crippled sister were exiled by their father in the first place was because they lacked sufficient warrior spirit. At 10 and 7, just after losing their mother.
Deltora Questturns out Lief has actually been the heir to throne the whole time, since his dad King Endon Swapped Roles with his best buddy Jarred before everything went to hell. So Lief has been a heroic prince risking his life at every corner without evening knowing how important he was, though when Endon kicks the bucket Lief is reluctantly upgraded to Badass King with everyone else supporting this decision despite Lief just wanting to be a blacksmith boy.
Being a series about kingdoms engaged in war games Dog Days has two current and one former examples: Gaul, Leaf, and Valério (who abdicated the throne in favor of his kingdom becoming a duchy). Leaf is probably the best example since he almost beat note as in literally one hit away from winningLeo in a one-on-one duel despite being several years her junior and lacking access to a Holy Sword.
If one wants to get technical, Vegeta's son Trunks is also a warrior prince, by virtue of being both a fighter and Vegeta's son. However, the only time he's ever called a "prince" is in a Non-Serial Movie (by a Saiyan that had survived the purge), and he doesn't seem to consider himself royalty by any stretch.
Going further, Vegeta's descendant, Vegeta Jr. from Dragon Ball GT might qualify as royalty as well. Though it's unlikely he even knows about this connection.
Technically, Gohan and Goten are this, as their grandfather is Gyū Maō (the king of Fry-Pan Mountain), making Chi-Chi, their mother, a princess. (Though, like Trunks, they were never really referred to as a prince.)
If you wanna get further technical, Frieza is this as well; his father is King Cold, ruler of the planetary empire he'd constructed for himself. For some reason, Frieza prefers to give himself the title of "Lord" over "Prince" perhaps to keep from reminding himself he's second-place in the organization.
Mystogan from Fairy Tail was later revealed to be one these.
All over the place in The Five Star Stories, due to a large number of the galaxy's royals being descended from ancient Super Soldiers and inheriting their powers.
For that matter, his half-sister Mei Chang is technically a female version. A very, very cute female version.
The kings and other royals of Ancient Belka in Lyrical Nanoha such as Sankt Kaiser Olivie and Ixpellia, what with being Persons Of Mass Destruction who personally fought in the wars of that era. While the kingdoms in question haven't existed for hundreds of years, Vivio, Einhart, and Victoria are all direct descendants of Belkan royalty.note Vivio is actually a clone of Olivie, but it's treated as the same thing. All three of them are highly skilled combat mages on the tournament circuit.
If you accept that he is Gihren's son/clone than Mobile Suit Gundam ZZ's Glemmy Toto is also one of these, acting first as a grunt mobile suit pilot, than as a commander, and finally as leader of his ownfaction
Also, Char Aznable, a.k.a. Casval Rem Deikun, is a prince from the Deikun family, and one of the most skilled pilots in the entire Universal Century.
Zechs Marquise/Prince Milliardo Peacecraft from Mobile Suit Gundam Wing. Although given that his kingdom, the Sanq Kingdom, was heavily pacifist in its ideals, he considers himself as a traitor to his family for becoming a warrior, and considers himself to have given up his royal identity.
The later chapters of the Magic World Arc in Negima! Magister Negi Magi revealed that Negi Springfield's Missing Mom is Princess Arika of Old Ostia. This would thus make him one of these. This had been foreshadowed all the way back in Chapter 15, when most of the class believed him to be a prince because they overheard him saying that he was looking for a partner. By extension, this would mean his grandson/clone Touta from UQ Holder! also qualifies.
The three Merman Princes; Ryuboshi, Manboshi, and Fukaboshi from Mermaid island are strong and won't take any shit from humans, though they just end up as punching bags for the Big Bad anyway.
Nefertari Vivi could be considered a Warrior princess since she did join a criminal organisation and stop a civil war to save her country. Subverted, however, combat-wise: she Can't Catch Up when it comes to the Straw Hats, so Vivi is closer to Princess Classic.
Though as later revealed, he is in fact a prince who was exiled due to being too pretty.
Kyros, the toughest gladiator in the entire world married the crown princess of Dressrosa, though he was technically never a prince since his wife forfeited her title to be with him (with her father's blessing).
Some asshole prince named Bellete attacks Ivankov in Impel Down only to be turned into a woman, technically making him a Warrior Princess.
Ace is the son of ex-the King of Pirates The Captain Gold D Roger, so that makes him a prince of some sort, but Ace never took the king title as General Ripper Akainu lava-punched Ace through the chest.
Sanji calls himself "Mr Prince" due to his tendency to rescue helpless babes and burst in Just in Time to save the day, but most people see this as him being full of himself. Zoro often says he is the "Prince... of the dumbass kingdom" prompting Sanji to fight him... but it turns out he is actually a prince! Specifically, Sanji is the third son of the Vinsmoke Family and Germa Kingdom and was considered the least warrior-like of his siblings and was punished dearly for it leading to Sanji getting disowned and fleeing his kingdom. But during his thirteen-year absence Sanji Took a Level in Badass (and took a cooking course) and declaring to King Judge that he wouldn't take any shit anymore and blows his father's mind when he actually saves them from Big Mom.
Vinsmoke Ichiji, Niji, and Yonji are warmongering sadistic Princes who rely on DNA and power suits to conquer nations as opposed to Sanji, who normally relies on his strength and skill to help people. Sanji is one of only two decent human beings among in the family (the other being his Warrior Princess older sister Reiju).
Ashitaka in Princess Mononoke is the prince of the Emishi, and is a brave and skilled archer willing to take on a rampaging demon to protect his people. He's cursed by the demon in the process, and has to accept exile from his people in order to go in search of a cure.
Prince Endymion is no slouch when it comes to battle, though he is not as powerful as his beloved. In fact, the "prince" form is stated to be a greater power than his "Tuxedo Mask" form specifically for this reason.
While the other Sailor Soldiers can be counted as Warrior Princesses, having been princesses in their previous lives, Sailor Mars deserves a special mention since she was given the title Soldier of War by Neo Queen Serenity, and she is indeed one of the strongest of the Inner Soldiers.
Snow White with the Red Hair: Prince Zen is an accomplished swordsman who participates in training the soldiers at the fortress of Raxd and has been trained since childhood alongside the knights group at Sereg. His older brother Izana is one of the country's best swordsmen, a decent archer and has proven himself a gifted strategist and tactician.
Granart's people, the catfolk, have a proud warrior culture and as their princess, she was trained to be the greatest warrior among them. Whereas the other ring princesses prefer to hang back and use magic during battle, Granart gets right in the thick of it with her sword, cutting her foes to pieces.
Prince Marse of the Gisaras Empire is a skilled swordsman. He teaches Satou how to wield a sword and fights alongside him for much of the series. Marse's elder brother, Prince Sluder, is a Frontline General in the Empire's military.
Tsubasa -RESERVoir CHRoNiCLE-'s Fai is technically this. Though not back in Valeria due to the whole tower and valley disaster but in Celes. Since he was adopted by Ashura-ou he was the prince, or at least the king's ward, and he went out to help the citizens and fight "monsters" regularily.
Van Fanel in The Vision of Escaflowne. He has to be, given that his country's tradition requires him to kill a dragon in single combat before he can ascend to the throne.
Princess Allura, particularly after she inherits the Blue Lion. The only reason she doesn't shoot Lotor once is she hasn't received the training to shoot first, think later.
Prince Lotor would qualify since he is royalty, and one of King Zarkon's top military commanders.
The Pharaoh from Yu-Gi-Oh!, albeit with children's card games that during certain duels summon mystically mighty monsters instead of swords or guns.
, and is a brave and skilled archer willing to take on a rampaging demon to protect his people. He's cursed by the demon in the process, and has to accept exile from his people in order to go in search of a cure.