Besides certain elements (such as crystals, Chocobos, summons, monsters, Cid, etc.) every Final Fantasy resides in their own individual universe. But so many parallels exist, it seems like they are all connected in some way.
Here are a few possible combinations for how each Final Fantasy universe is connected:

Final Fantasy I
Due to the timeline, Garland might have created several paradoxes that would have spurned many alternate worlds. Yet, after defeating Garland, they never would have existed.

Final Fantasy IV
Appropriately, since space plays a pretty big part in the plot, it’s no surprise each Final Fantasy universe. The proof comes from the divisie After Years sequel. During the final dungeon, you end up defeating familiar bosses (that reside inside of crystals) from the other games. What does this mean? That other Final Fantasy worlds exist as planets.

Final Fantasy V & VI
Due to each having Gogo, one can postulate the interdimensional rift exists in both. The interdimensional rift is what connects the characters in Dissidia Final Fantasy (at least, that’s what I think). Either way, perhaps the interdimensional rift is a wormhole that connects each game.

Final Fantasy VII
The Lifestream is Gaia’s afterlife and also the “force” enveloping their world. Yet, it also seems to connect multiple worlds. Cloud arrives in Ivalice from the Lifestream. Perhaps the Lifestream has warp holes?

Final Fantasy VIII
Each timeline, through the right amount of infinite combinations, could have been another Final Fantasy world. Ultimecia tried to stop this temporal evolution, making her god over every Final Fantasy.

Final Fantasy IX
Weaves the series together through the crystal.

Final Fantasy XII
Final Fantasy XII is Final Fantasy Tactics’ golden age. But other Final Fantasy Tactics games tell of Ivalice as a children’s story. If Ivalice were just a book series, the other Final Fantasy universes are books in a fantasy series.

Final Fantasy XIII
At the end of Lightning Returns: Final Fantasy XIII, Lightning creates the new world. But Final Fantasy XIII-2 talks of multiple world. Who know how many different timeline Lightning created the world?

Final Fantasy XV
Final Fantasy XV opens up the possibility that every Final Fantasy game’s is another’s afterlife.