Emergent AI behaviors
Best example of the game that uses Utility AI is The Sims. You can basically create a set of actions agent can do depending on its current needs and let agent chose what's best for him to do at given time by modeling behavior after Maslow's hierarchy of needs.
Rouglike games can use it to make procedurally generated agents perform unique life-cycles based on PCG agent stats.
Strategy games can use it to let factions and units evaluate certain strategies that will then be run by other decision makers (using hierarchical approach).
Branchless dynamic dialogues
You can bring life to dialogues with NPCs by making NPC choose a line that fits best current situation and facts about the world. Imagine talking with NPC before and after result of some major game event or some crazy fact heard about one of your battles and using that knowledge to drop some comment about it or ask you questions about what happened.
Emergent storytelling and adaptive world events
When making a game focused on replayability your goal is to make player experience the game differently on each playthrough, for that you might want to forget about scripted events sequence and let game spawn game events that based on the game state or even player "fun" score to keep pacing that will make player engaged.
In general you can use Utility AI to systems that are meant to be unpredictable, provide unique experience to the player or even produce viral moments for players to share with others.