Dueling Games: Before Square and Enix merged, Final Fantasy and Dragon Quest were very much rivals of one another. Even today (mainly in Japan), there is still some rivalry over which series is better.
And within the Broken Base of Final Fantasy fandom, while many different games' fans are at each other's throats, likely the best-known rivalry is between fans of Final Fantasy VII and Final Fantasy VI, with many of the latter resenting the former's popularity, which is believed to be undeserved as compared to their own game, and the former thinking (if they care at all) that the title of best FF game is theirs and the old-school fans need to get over themselves already. This usually manifests itself as fighting over which game had the coolest villain.
Meaningful Name: A lot of the names in the FF world draw upon mythology, religious beliefs, and fiction. A good example are all of the summons, who are named after mythical figures, places, or objects such as Leviathan, Kujata, Shiva, Hades, and Ark to name a few.
Some of the weapons are named after legendary ones such as Excalibur, Masamune, Gigas, and so forth.
The franchise itself. At the time of its creation, as mentioned above, the first game was intended to be Squaresoft's last hurrah; a game meant to be the 'last word in turn based RPG's'. Fortunately, the game was so popular that it saved Square, and they went on to make more and more games, creating a franchise that's still beloved by many. But the name has never changed: it's still called Final Fantasy, as an homage to the game that saved them.
According to Kazuhige Nojima (albeit in a way that he could deny it if needed) Final Fantasy X and Final Fantasy VII are connected - a side quest of FF X-2 has Shinra talking about the possibilities of harvesting the energies in the Far Plane energies, but he laments that technology would not be around for at least 300 years to do so. In the X-2 guide it is stated that Square had always planned on having the worlds interconnected somehow and that X-2 is a huge hint that after space travel is up and running the inhabitants of the world travel to the far distant world of Gaia, FF7's world, and find the 'life stream' where 1000 years later the descendants of Shinra found the Shinra Electric company and set off events of Final Fantasy VII.
Before Square got into the Final Fantasy franchise, they tried their hand at an arcade styled racing game called Rad Racer on the NES. The music composed for the game was done by Nobuo Uematsu, an unknown composer at the time until he started to make music for the Final Fantasy franchise.