How do I say ‘I’m hungry’?

Chinese usually frames hunger as a state that has arrived, which is why 了 sounds natural here.

Chinese frames hunger as a state that has arrived — the 了 marks the change. Without it, 我很饿 describes a general condition (and sounds slightly more written). The playful 快饿死了 follows the same 死了 intensifier pattern as 累死了: literal “starving to death” with zero literal meaning, just conversational exaggeration among people you know.