Angel: Cordelia Chase ascends the throne of Pylea within 48 hours. "Off with their heads", indeed.
Power Rangers Wild Force has Princess Shayla as their mentor. No particular plot-relevant reason for her to be a princess.
Inverted in Tin Man: True, DG is a princess and the best hope of the resistance, but it's also all her fault that there's a need for a resistance in the first place! She also seems to conspicuously lack the floofy dress and tiara. She never wanted to be a princess or even dreamed that she was. She takes after great-grandma Dorothy, who was quite the Action Girl!
Xena is a princess in honourary title only. Revealed in a flashback, Xena's mentor says that Xena will be her "warrior princess" fighting for love, peace, and all that jazz — thus explaining away the show's title.
Gabrielle, her sidekick, is an Amazon princess, sorta. She gets to be an actual Amazon princess by the Queen of the Greek Amazons' younger sister and heir transferring her right of caste (a.k.a. princess-hood) to her before dying; she then gets to be Queen further on.
Kings is good for this. In a court filled with adulterers, corruption, misdirection and all manner of levels of deceit, only Princess Michelle cares about the health care of the people and is willing to sacrifice. Unfortunately for her, Good Is Dumb.
Delenn in Babylon 5 is a Satai and a descendant of Valen, and just acts like a princess.
Played straight in Merlin with Princess Elena, who herself is a Deconstruction of a Tomboy Princess but is nevertheless called a "princess" despite her father only carrying the title of "lord." It's played even straighter with Princess Mithian, though she's a case of Princesses Rule. Otherwise averted throughout the rest of the series. High-born ladies such as Morgana and Vivian are referred to as "ladies", despite them being the daughters of kings though in Morgana's case, her paternity was kept a secret, and Guinevere is a servant girl who jumps straight to the title of Queen when she marries Arthur.
In Diplomatic Immunity, Leighton's love interest Leilani is daughter to the brother of the king which technically makes her a princess. Leighton must have a thing for princesses because before the show's beginning he had a public indiscretion with one. And in another episode Leighton gets persuaded to join the Aru Tiki order upon hearing that tradition says he would get his pick of beautiful island princesses.
Used as a plot point in "The Armageddon Factor". The serial's main protagonist (apart from team TARDIS), Princess Astra, turns out to be the final segment of the Key to Time, and sacrifices her human form to help the Doctor complete his quest. After the Doctor destroys the Key to Time at the end of the story, the last segment becomes Astra once again.
The whole premise of Princess Returning Pearl revolve around the adventures of the fake princess Xiao Yan Zi (who even becomes a real princess when she gets married to the Prince Charming) and the real princess Zi Wei.
One episode of Charmed revolved around fairies. Thistle, the fairy being protected by a little girl, is of course a princess too. The episode "A Knight To Remember" Gender Flips this by giving Paige a prince summoned from the past. In this case, Paige's past life was attempting to exploit this trope by marrying the prince and seizing control of his kingdom. The episode does feature another woman in the past who is referred to as simply "Lady" Julia - though she would presumably become a princess once the sisters saved her.
Pops up a couple of times in Sabrina the Teenage Witch. When Sabrina is preparing for her wedding she becomes obsessed with being a princess. To the degree that she summons Cinderella for advice. It's also given a Gender Flip in the season 1 finale. Sabrina is locked in a tower by a troll. And it's legal. The only way to save her is if a Prince rescues her. Said troll does dress Sabrina up like a Princess Classic though.
Slater actually gets a Princess for a love interest in an episode of Saved by the Bell. It's somewhat Played for Drama as Slater worries that he doesn't fit into her world - but ultimately gets over it.