Can we assemble a list of women with the title of “Princess” in Science Fiction?
I’ll start–
[ul]
[li]Leia Organa[/li][li]Dejah Thoris[/li][/ul]
Princess Vespa - Spaceballs
Princess Aura, Flash Gordon. I’ll be in my bunk.
I had thought her name was Ardala. Turned out I was confusing her with the similarly attired princess from the Buck Rogers TV series.
Didn’t realize when I first saw the series how much of an eyeful Dr. Huer was getting. Then again, I was like 6 or so.
Alusz Iphigenia Eperje-Tokay.
Okay, it’s obscure, but she counts! She’s from Jack Vance’s “The Killing Machine,” second of the five-book Demon Princes series. (The name sounds like fantasy, but it really is SF.)
To be even more obscure, there’s Gillian U, who met Prince Frederick of the Nashuite Empire in Alexei Panshin’s novel “The Thurb Revolution.” Their marriage was alluded to in a sequel.
Wasn’t Meseriphine Sursamen/VIIIsa Djan Seriy Anaplian dam Pourl an actual princess? Albeit one long removed from the family intrigues, both in distance and time, considering she was a Special Circumstances agent.
I still think Matter was Iain Banks’s attempt at writing a Regency-era drama—I think it’s required of every writer from the U.K.—but set IN SPACE. Most of the book, I kept wondering, “So when do we get back to the Culture again?”
Princess Karina from The Ice Pirates
Princess Irulan from Dune
If you’re inclined to think of superhero comics as sci-fi, there’s Princess Diana.
Let’s not forget her conniving little sister Princess Wensicia Corrino.
And I suppose Ghanima would count, too, although with their age at ascension to the throne, she wasn’t a princess for long.
Princess Amidala of Thneed, Star Wars
Princess Aeka
Princess Sasami
From Doctor Who: Princess Astra, a.k.a. the living, breathing sixth segment of the Key to Time (as well as the living ‘blueprint’ for Time Lady Romana’s next incarnation.
Elaan of Troyius, Star Trek
Princess Nausicaä: Nausicaa of the Valley of the Wind
Well, it would sound like fantasy - you can thank Kokor Hekkus for that. He spent centuries reshaping the whole world into his very own medieval adventure playground, the silly man. There are other ways to leave a lasting impression on the universe. 
Princess Kareen Vorbarra, mother of Emperor Gregor, from the *Vorkosigan *books.
And who could we forget the Imperial Regent Princess Alia Atreides.
The Martian princesses Illana, Alura, and Glurya, from the Buck Rogers comic strip.
Duare of Vepaja, from Burroughs’ Venus series.
Also from Burroughs’ Mars:
Tara of Helium
Thuvia of Ptarth
Llana of Gathol