Of course we do! But particularly looking to physical gods, they tend to only appear in Eorzea, due to the aether.
[That's a lot of words that she decides not to explain, and she talks really fast to get everything out. At least her excitable tone is still pretty coherent.]
They vary a fair bit, but the main theme is that their worshipers manifest them into the physical realm through prayer and sacrifice. There are two exceptions I can think of, but I'm afraid I can't explain them very well.
Anyway! They can also brainwash normal folk into selling their souls to them, which makes them all the more difficult to fight even aside their other divine properties.