Ceruleum is essentially magical gasoline; as such it can be used for all the purposes gasoline is used and then some, and serves as the backbone of the Garlean Empire's power supply. All Garlean machina uses ceruleum unless otherwise noted (the Ultima Weapon used the Heart of Sabik, f'ex; even then it still supplemented its power supply with ceruleum if I remember right).

Though they can use magic, the Eorzeans still use ceruleum for certain applications; airships still run on the fuel, and all of Cid's consumer products implicitly use it as well.

Alternative fuel sources (steam, electricity) are in their infancy; ceruleum is more efficient, and the Eorzeans with the funds to develop such technology (Ul'dahns) are held back by their plutocratic government. (There is the beginning of a steam train in Thanalan, but because it would be a threat to Lolorito's business, it's incomplete and underfunded.) Ala Mhigo was said to be the most technologically advanced city-state before it fell to the Garlean Empire, but I didn't really see evidence of such during our time in Gyr Abania.

Past that, elemental crystals can presumably be used to replicate the effects of the element they are attuned to; a lightning crystal could be considered a battery, f'ex.

Most transportation in Eorzea is still done via chocobo and chocobo-drawn carriages, due to wealthy businesspeople (Lolorito) having a stake in it. Shipment of goods is done primarily via sea routes due to it being less dangerous and costly, however.