Simple deterministic AI behavior
Indie games with small number of AI agent states, usually platformers or fast-paced games like shooters or bullet hells - in general games that doesn't need long-term or strategic planning and they have to make decision fast to adapt to quickly changed environment.
All modern game engines use FSM to manage animations, transition between them also contains information about blending between states to not make states snap from one to another instantly.
Game states / game modes
Imagine you have a game session with several states: Overworld, Battle, Shop, Crafting. You might use FSM to manage changes between these different game modes.