Despite their sci-fi world, the Jedi feel like old-fashioned knights. No, they don't wear bucket-looking helmets. No, they don't ride space-horses. No, they don't (often) say "milady."
They're knight-like because of their weapon of choice. Lightsabers are basically high-tech versions of swords or katanas, and the Jedi are basically space knights—or, better yet, space samurai. The imagery of the two together instantly brings to mind romantic stories of bygone ages where chivalry and courage were the currency of warriors that fought with honor to protect the peace of the land.
Hey, they're called Jedi knights for a reason.
The organization of the Jedi also feels like it belongs to these romantic eras. The Jedi live their life by the "Jedi Code." Although we don't learn much about this code in The Phantom Menace, we hear enough to understand it is a set of principles and practices that determine how Jedi are to act and behave.
For example, Mace Windu reminds Qui-Gon that he can't take a second apprentice because "the code forbids it." This code is analogous to bushidō, the code of conduct of the samurai, which literally translates into "way of the warrior." (Source).
It can also be analogous to the knights' Code of Chivalry from the European Middle Ages. (Source)
As the above codes suggest, the Jedi are warriors, but they're also the peacekeepers of the Galactic Republic. When Qui-Gon learns the Trade Federation plans to invade the Naboo, his first thought is to "warn the Naboo and contact Chancellor Valorum." He then spends the rest of the film protecting the Queen from the droid army and the Sith. He gains no reward; it's simply his duty to protect the innocent and bring wrongdoers to justice.
Of course, the image of the Jedi draws more from the Hollywood version of the Middle Ages and the days of the samurai than the actual reality. In truth, knights and samurai lived in brutal times… and their customs were a sign of those times.
For example, the First Crusades saw knights perform some very unchivalrous acts, including an ethnic cleansing of Jews and Muslims after the Siege of Jerusalem of 1099. (Source)
On the other side of the world, the samurai practiced a custom of taking their enemies' heads to present to their warlords for honor and reward. (Source).
(Dang. The Phantom Meance would be a very different movie if Qui-Gon bathed in the blood of his enemies while demanding payment for the heads of those he had slain on the battlefield.)