FFXIII - no spoilers in comments, please!
Hecatoncheir - I donno what this is in FFXIII, but in Greek mythology, hekatoncheires, "hundred-handed", are giants with a hundred arms and fifty heads who unleash the storms of Tartaros. They fought on the side of the gods of Olympus against the Titans. They appear in Hesiod's Theogony.
While choreographing the Sin vs. Veganun battle in LHaD, I looked up Vegnagun boss battles and discovered all its attacks are Latin quotes.
Noli Me Tangere (tail-swipe) -- "Don't touch me" Jesus to Mary Magdalene, John 20:17, vulgate edition
Dies Irae (rain of white energy) -- "Day of wrath" name of a Catholic hymn about Judgement Day.
Lacrimosa (blast of orange fire) -- "teary" in the sense of "deserving of tears"
Mors Certa (red and black burning miasma) -- "Certain death"
Pallida Mors (sphere of white energy forms between tusks, gets lobbed like sling shot) -- "Pale death" from:
pallida mors aequo pulsat pede pauperum tabernas
regumque turris. -- Horace Odes 1.14-15 "Pale death knocks with equal foot [i.e. in the same way] on the hovels of poor men and the towers of kings"
praetor is "one who goes before" -- government officials in Roman Empire in charge of administrating law court system over a large area (Italy, the provinces, one praetor for Rome).
Auron - I can't tell if this is a Greek ending slapped onto Latin aurum, "gold", or if his name comes from Aaron, brother of Moses.
Tetra shows up on some magic items, from Greek prefix for "four". Items with four slots or particularly rare items are tetra. (Hence my using "tetra-grade" as Rikku's term for "really strong.")
maester looks like a Latinized version of master, or perhaps a mutation of magister, "teacher, professor, master, doctor".
One-winged Angel lyrics come from Carmina Burana. See my old post with lyrics.
Sephirot --Hebrew. the ten attributes/manifestations through which God reveals himself in the Kabbalah. Each sephirot was supposed to manifest at a different time from weakest to most potent, and they're connected with the powers of creating the world. (In-depth article on the ten sephirot)
Aeris - probably from Latin aer, "sky, air" Mako - I'm assuming this is a slight variant on mahou, magic, a Japanese borrowing from English.
ETA: see comments below on aeris/th and mako; we've got someone who can read Japanese to untangle them for us!
The first two lines of Liberi Fatali (the opening theme) are nonsense (Tagamet, Prilosec, or some such ;) ) but the rest of Liberi Fatali ("children of fate") is an original Latin song composed for the game. Lyrics and translation here.
Final Fantasy Characters: Name Origins suggests many more, including a reminder (duh, should've noticed) that Lucretia is the archetypal rape victim in Roman legend. Also of interest: Tifaret is another of the Sephirot in the Kabbalah, Reno could be from Latin leno, pimp (not sure on that, but it's amusing), cait sith = "fat cat," a figure in Irish folktales.