They definitely seem to like to draw quite heavily on the mythology of Star Wars for their stories. Here are the references that I've noticed:
- At least three of the games-- Final Fantasy II, Final Fantasy VI and Final Fantasy XII focus on groups of rebels who are attempted to topple an evil Empire. Final Fantasy VII also shows this plot to some degree, except that it's an evil corporation. Of all of these, the influence is perhaps most striking in Final Fantasy XII, which focuses on the story of Vaan (Luke Skywalker, though thankfully he doesn't have a father in the Empire), an orphaned boy who dreams of taking to the sky and who often seeks advice from Old Dalan (Yoda.) Along the way he encounters Balthier (Han Solo-- fighter pilot type and somewhat shady individual who has a heavily modified ship, the Millennium Falcon... sorry Strahl) and Princess Ashelia Ba'nargan "Ashe" Dalmasca (Princess Leia) of the Insurgence ("Amalia": Resistance!), who together with others fight to topple the Archadian Empire. Balthier's father is Cidolfus Demen Bunansa (Darth Vader, very loosely.) Vayne Solidor (okay, admittedly no Palpatine) slays his own father, Emperor Gramis.
Penelo, Fran, Basch, Larsa, Al-Cid Margrace, Lord Reddas/Judge Zecht and Judge Bergan/Noah-- these I can't fit into the Star Wars mold, though if anyone else wants to try, they're welcome to it.
- Since Final Fantasy VI, Biggs and Wedge are recurring characters in the games. Biggs Darklighter and Wedge Antilles were Rebel pilots in the original Star Wars film (Episode IV: A New Hope.) Biggs was killed in space combat, but Wedge Antilles survived and has since risen to some status in the New Republic / Galactic Alliance in the Star Wars Extended Universe saga. In the FF games, Biggs and Wedge have appeared in varying forms, but were most prominent as part of well, a rebel group named AVALANCHE in Final Fantasy VII. Many were also entertained by the antics of Biggs and Wedge in FFVIII.
- In Final Fantasy IX, Necron uses the words "Fear leads to anger... anger leads to hate... hate leads to suffering..." These were Yoda's insightful and predictive words to Anakin Skywalker (later Darth Vader) in Episode I: The Phantom Menace.
That's all I can think of for now, though if anyone else knows of any others, overt or covert, post them here. Curiously, I only know of one Star Trek
reference within the FF series, and that's in IX when one of the people who you ask about the potion tells you "Dammit, Jim! I'm a doctor, not a miracle worker!"