Garland in IX is the same Garland as FFI, he was just trying to complete what he started... somehow.

Squall is a descendant of Leon and bears his full name as a surname.

Yunalesca is the Cloud of Darkness.

Most stories mention "(x) thousand years ago another incident happened", those incidents are the other FF games where warriors defeated great threats to the planet.

The "ancient weapon" that the empire uses in FFII, a fortress concealed by a tornado, is quite obviously The Bahamut from FFXII.

King Bahamut in FFIV is the same from FFI - the dragons just became even more isolated to the point where they had to leave Earth. Also, Vayne is Bahamut.

The Lunar Cry - monsters coming from the moon in FFVIII is somehow connected to the moon's special stuff in FFIV.

FFVII may be an origin story of how the crystals came into being - they were just high concentrations of the life energy of the planet, crystalized into Huge versions of Materia. The four huge materia in Bugenhagen's observatory are pretty obviously the 4 Crystals. As in traditional 4-crystal-games (FFI, III, V), destroying them negatively effects the planet's life force, or its manifestations such as wind, earth, sea. As such, the huge materia in FFVII also represent this - Junon's Underwater Reactor is sea, Corel's is Earth, Nibelheim's is Fire (they burn down the town afterall) and Fort Condor's is Wind. It's pretty simple really.

So looking at that in the odd-numbered games, and looking at FFIX's story of two planet's trying to merge together, my theory is that the odd-numbered games take place on Terra, and the even numbered games on Gaia, or vice-versa. While FFIV and FFVIII also have crystals, they number not 4 (there are 16 and 1, respectively), and not related to the elements, so they still stay in the non-crystal world. Some games don't fit nicely into that picture, and I would say that's the games that take place during/after the assimilation of the two.

To support this, Garland used the idea of Black Mages from the memories of the crystal of Terra, and Black Mages with that appearance and purpose appear in all the odd numbered games: I, III, V, and even VII - Cloud has blonde-spikey-hair instead of a yellow-pointy-hat and a blue outfit, he starts off with beginner's offensive spells of Ice and Lightning, and has the strongest Magic statistic in the game outside of Aeris. Cloud is a Black Mage who was genetically altered through the SOLDIER process with Jenova cells - hence his sword proficiency and high strength.

Of course this is all BS - the developers have stated FFIV and FFIX to be tribute games with embodiments of and references to its predecessors, and every other game has paid homage to a lesser degree as well. But who knows, maybe one day Sakaguchi or Hiromichi Tanaka and Koichi Ishii (the real creators of the idea of Final Fantasy) will come out and say it's a loosely connected saga after all.