here's just a short list of similarities drawn from early FF titles into later titles including XI:.

FFI - The uber-original. Most things derive from here.
FFII - Dreadnought airship controlled by the evil empire (oh, and evil empire/rebel faction) Magic & machine hybrids. Passwords to gain trust. Underworld, Cid, Chocobos
FFIII - Castle was floating according to ffI lore, but first with a floating continent. many staple creatures first seen here, like summons. Moogles! Job-change system, Crystal Tower
FFIV - interactive mounts, Active-Time Battle system. Multiple breeds of chocobo.
FFV - parallel worlds addressed, void explicitly addressed, intro to Gilgamesh. Minigames added. Job system further expanded
FFVI - Heavy expansion to magitech, 1000 year old mage war. Magicite used to gain power by equipping gems and fighting monsters (similar to vii materia). cinematic cutscenes. Coliseum battles. Ultros. Weather system (Mog). A crapload of stuff.
FFVII - characters graduate from sprites to 3d models- Gold Saucer, materia attachments in gear sockets, chocobo breeding/racing
FFVIII - upgrade system for gear
FFIX - Feud between 2 uber powerful summons: Bahamut & Alexander. Mist/miasma as a source of magical beasts threatening the world.
FFX - Macalania woods much like corrupted aether east of camp drybone. Full CG cutscenes & voice acting
FFXI - Shantoto event, races of Vana'diel closely based on player races in xiv
FFXII - Hunt system
FFXIII - Lightning event

I'm sure im missing a LOT and may expand later... but this is just off of the top of my head.