Male frogs croak to mark out their territory, to threaten other male frogs and to call females to them.
Loaches make clicking noises when frightened or trying to scare off other fish. My loaches click like crazy during feeding time.
I've seen my pleco & catfish get into a scuff and heard a strange screech type sound when this happened. I'm sure that's the cat or pleco's way of saying, "Back Off".
As far as our barbs, tetras, cichlids,etc. I'm sure visual cues are the way they communicate. Body movements, postures, colors and color patterns are what I notice my fish displaying. My rams will color "up" or color "down", depending upon what message they want to get acroos.
As guri states, fish also communicate by releasing chemicals called pheromones. I'm always amazed that fish can "smell".