A character named Cid features in every single one of the main (numbered) Final Fantasy games. The character was first introduced in Final Fantasy II (1988) (although when Final Fantasy (1987) was ported to the PlayStation, he was retro-ed into the game). However, Cid is never the same character from game to game, although he is often the owner of the airship.
Several of the words in the game derive their origins from Norse mythology. Midgar, for example, is derived from the Norse word "Midgard", which is where the gods put humans to protect them from the giants. "Nibelheim" is derived from the word "Niflheim", which is the land of the dead, and also literally means "fog home" or "mist home" (important insofar as the town is Cloud's home in the game). One of Cloud's swords is called the Ragnarok, which comes from "Ragnarök", the Norse doomsday.
Final Fantasy VII is the first game in the series to suggest the origin of monsters; Shinra experiments with mako energy on live test subjects. Previous games omitted any sort of explanation, with the existence of monster never questioned by the characters. Thus far, only four games in the main series have provided a rationale for the existence of monsters: Final Fantasy VII, Final Fantasy VIII (1999), Final Fantasy IX (2000) and Final Fantasy X (2001).
At the beginning of the game after blowing up the reactor, cloud travels through town before being confronted by spoilers. A poster on a building reads "Mt Kolts". Mt Kolts was a mountain in the previous game, Final Fantasy III (1994).
Beginning with this game, the games had the same number in the title in both the American and Japanese releases. Prior to this, only three games in the series had been released in the US; leading to Final Fantasy III (1994) being released under the title Final Fantasy III. Starting with this game, Squaresoft fixed the problem once and for all by releasing the game worldwide as Final Fantasy VII. They also went back and did "reissue" packages using the correct, original Japanese numbers for the previous games in the series.
The trivia items below may give away important plot points.
Rumors persisted for years following the game's release that the character Aerith could be resurrected. Various insanely time-consuming methods were proposed, and it was later claimed that it was only possible in the Japanese version by buying a rose when Cloud meets Aries at the beginning of the game, and was cut from the US version due to time constraints. These were all finally put to rest when Tetsuya Nomura was interviewed about the making of the game by UK video games publication "Edge". He stated that "[T]he world was expecting us to bring her back to life, as this is the classic convention. But we did not. We had decided this from the beginning." Aerith's death was intended, in part, to be a response to the dramatic cliché of the "meaningful death", which Nomura considered unrealistic. Nomura has also always maintained that if the game is ever remade, Aerith will die in the remake.
Although the planet on which the game takes place is never named, nor does it resemble the Earth's world map in any way, the planet is actually meant to be the Earth. This can be seen in Safer-Sephiroth's attack where he destroys planets such as Pluto and Jupiter, and eventually blows up the sun. The explosion reaches Earth and attacks the party. Other than this, there is nothing to support the argument that the game is set on Earth.