Holy CRAP! FFT and FF12 share the same world?!

[WhiteArchmage]

It's not "A" theory that a calamity wiped out the races in Ivalice (or at least drove them more heavily into hiding), it's in plain text if you check the background text in Tactics; amusingly, there's another Cataclysm aluded to in XII's bestiary, which makes it seem that Ivalice seems to suffer something similar to Eorzea, parhaps through similar reasons (more abuse of aether and such, less influence from Ascians...unless you count the Occuria and Espers/Lucavi).

The timeline is generally agreed (I forget if the Ultimanias have made it canon) to go: FFXII -> FFXII:RW -> FFT -> Vagrant Story -> FFTA (though afterwards taken to a Dream Ivalice) -> FFTA2 (with actual time travel taking Luso to some point after XII:RW). And before someone points it out: no, the maps aren't quite related (except possibly TA2 and XII) since said cataclysms have moved, raised or destroyed landmasses, efforts to paste one game's map next to another have been debunked by canon.

[CaesarCV]

That's mostly right, although I remember hearing somewhere that Vagrant Story isn't actually canon to Ivalice. When it was created all of the references were put in more for fun than to imply it's the same setting, which perhaps makes sense given how magic and the like work completely differently in that game. It's kind of a complicated mess since certain games (like Tactics) are more retroactively Ivalice than anything. It's...not always easy.