It's worth noting that the Prelude doesn't occur in every game (FFVIII for example). However, it's still a series constant, so to speak.

Some recurring motifs, beyond airships and Cids, include:

-chocobos
-moogles
-characters named Biggs and Wedge (starting with FFVI)
-certain weapon, armor, and accessory names (Masamune, Ragnarok, Ribbon [which was first headgear, then an accessory], etc.)
-Bahamut (summon starting in FFIII plus a role in FFI) and certain other summons, notably Ifrit and Shiva
-a number of spells (Flare, for example)
-various enemies (for example, Bombs)
-starting with FFV, and continuing in VII, VIII, IX, X, and X-2, the idea of superbosses

Then there are more limited motifs. For example, graveyards. FFV had a ship graveyard, FFVII had a train graveyard, and FFT had the Graveyard of Airships.